Abstract The present study is a numerical inspection of the natural convection with double diffus... more Abstract The present study is a numerical inspection of the natural convection with double diffusion in a tilted square cavity filled with a vertical bi-layered composed porous and an adjacent fluid. Isotropic and homogeneous porous layer is considered in this case study. The porous layer is saturated by an aqueous solution with a Prandtl number Pr = 7. The horizontal walls are considered impermeable and adiabatic, while uniform concentrations and temperatures are set on the vertical walls. The Thomas algorithm is employed to find a solution for the system of the governing equations. The divergence of the non-linear system is avoided by introducing under–relaxation factors. The effects of the various non-dimensional governing parameters namely the thickness of porous layer, Rayleigh number, buoyancy ratio, Lewis number, cavity inclination angle, and the thermal conductivity ratio on the thermo-solutal natural convection and the rate of mass and thermal exchange are highlighted and discussed. The predicted findings are given in terms of flow patterns, thermal fields, and iso-concentration lines. The variation of the velocity field, stream function, Sherwood number, and Nusselt number is also inspected. The numerical results show complex flow structure modifying the local transfer (Nusselt and Sherwood numbers).
In this work, bipolar fuzzy parameterized sets in conjunction with soft sets are studied. This r... more In this work, bipolar fuzzy parameterized sets in conjunction with soft sets are studied. This research focuses on the application of bipolar fuzzy parameterized soft sets (BFPSS), arising from association of bipolar fuzzy parameterized sets with soft sets. Some useful operations and fundamental properties of BFPSS are presented. Mainly, we aim to design a novel and comparatively labour-saving algorithm to see the efficacy of BFPSS. We discuss an application of our algorithm in pharmaceutical decision making problem based on effectiveness and harmfulness of certain drugs. However, the algorithm is equally applicable in other decision making environments as well where BFPSS arise. By preserving the structural implication of BFPSS, we compare our technique with a most recent algorithm to prove the significance of our method.
Abstract The vector borne diseases share a high percentage of the annual deaths reported by the w... more Abstract The vector borne diseases share a high percentage of the annual deaths reported by the world health organization. Due to the involvement of multiple factors and resistance of the vector to the treatment strategies, it is highly desired to design a safe, efficient and harmless control strategy. A state of the art computational framework for the Wolbachia induced “genetic-control-strategy” has been documented during this research. The process of mating and molecular identification is complex and expensive and different labs around the world are devoted to format a smooth implementation strategy of this approach. During this research, as a first step, data was collected, secondly, dynamic artificial neural networks, with the “tapped delay” lines are used for nonlinear filtering of the data and for the prediction of the parametric values of the novel mathematical model. To study parametric reliance of stable solutions and unstable solution we analyze stability and the corresponding thresholds desired for this study are documented. The study conducted during this research can prove to be useful in future experimental and theoretical studies, aimed to control the vector borne diseases.
Abstract In the existing numerical analysis is developed to impact of a closed space rectangular ... more Abstract In the existing numerical analysis is developed to impact of a closed space rectangular heat source on natural convective flow-through triangular cavity. The present problem is expressed as non-linear governing equations extended mathematical model is solved by engaging a Galerkin weighted residual process of a finite element scheme. Some investigation is acted for several Rayleigh number (Ra) at Pr = 0.71 on flow pattern and heat variation inside an enclosure. The resulting numerical clarifications of the query are exhibited graphically in phases of streamlines, velocity profiles, isotherms, Rectangular bar effectiveness, mean Nusselt number, and average fluid temperature. The acquired outcomes verified that a rate of heat variation progress with the rise of a Rayleigh number within a triangular cavity. Results are verified relating to a published work.
In the present paper, we construct the traveling wave solutions involving parameters of some nonl... more In the present paper, we construct the traveling wave solutions involving parameters of some nonlinear PDEs in mathematical physics via the nonlinear SchrÖdinger (NLS) equation and the regularized long-wave (RLW) equation by using a simple method which is called the (G'/G)-expansion method, where G=G(ζ) satisfies the second order linear ordinary differential equation. When the parameters are taken special values, the solitary waves are derived from the traveling waves. The traveling wave solutions are expressed by hyperbolic, trigonometric and rational functions. This method is more powerful and will be used in further works to establish more entirely new solutions for other kinds of nonlinear PDEs arising in mathematical physics.
In this paper, the therapeutic interactions are discussed with the aid of a mathematical model an... more In this paper, the therapeutic interactions are discussed with the aid of a mathematical model and piecewise differentiation technique. The model is based on the interaction between cell populations in therapeutic stress and cell populations in neoplastic transformation, referring specifically to triple-negative breast cancer (TNBC). The proposed computational approach provides an opportunity for the qualitative and parametric analysis of the clinical trials in question. The proposed mathematical model is based on the analysis of cell–cell interactions according to a logic that examines pathological stress and its influence on the dynamics of the cell population involved in tumor pathology. Detailed literature review and dynamical analysis of the proposed hypothesis are provided in this paper. The existence and non-negativity of the solutions are exploited, the hypothesis is stabilized; it is then further demonstrated with the aid of the piecewise derivative and the relevant applica...
Abstract This paper retrieves optical solitons to the perturbed Biswas-Milovic equation which des... more Abstract This paper retrieves optical solitons to the perturbed Biswas-Milovic equation which describe the propagation of pulses of various types in optical fiber. Hamiltonian type perturbations are considered with maximum intensity. Kudryashov's law is studied. The Jacobi elliptic function solutions are found using the unified auxiliary equation method. Dark solitons, singular solitons, bright solitons, combo singular solitons and combo dark-singular solitons are obtained.
Abstract This paper studies highly dispersive optical solitons in birefringent fibers with Kerr, ... more Abstract This paper studies highly dispersive optical solitons in birefringent fibers with Kerr, quadratic-cubic, polynomial and non-local laws of refractive index. Three integration schemes adopted are Riccati function approach, sine-Gordon function technique and F -expansion method.
Journal of the Egyptian Mathematical Society, 2017
In this research, we construct the traveling wave solutions for some nonlinear evolution equation... more In this research, we construct the traveling wave solutions for some nonlinear evolution equations in mathematical physics. New solutions such as soliton solutions are found. The method used is the generalized Kudryashov method (GKM). We apply the method successfully to find the exact solutions of the following nonlinear integro-partial differential equations: the (1 + 1)-dimensional integro-differential Ito equation, (2 + 1)-dimensional integro-differential Sawada-Kotera equation and two members of integrodifferential Kadomtsev-Petviashvili (KP) hierarchy equations. These equations have numerous important applications in mathematical physics as well as in engineering. This method is efficient, powerful and simple.
International Journal of Computer Mathematics, 2018
ABSTRACT In this paper, we use the extended trial equation method (ETEM) to construct the exact s... more ABSTRACT In this paper, we use the extended trial equation method (ETEM) to construct the exact solutions in many different functions such as the trigonometric function, elliptic integral function, rational function, hyperbolic function and Jacobi elliptic functions for nonlinear evolution equation in mathematical physics via the fifth-order modified nonlinear Kawahara equation. In this method, the balance number is not constant as we have shown in other methods, but it is changed by changing the trial equation derivative definition. This method is powerful, reliable, effective and simple for solving more complicated nonlinear partial differential equations in mathematical physics.
In this article, we construct the double soliton exact solutions for some nonlinear partial diffe... more In this article, we construct the double soliton exact solutions for some nonlinear partial differential equations in mathematical physics via (2+1)-dimensional Painleve integrable Burgers equations, (2+1)dimensional breaking soliton equations and (2+1)-dimensional Nizhnik-Novikov Veselov equations. We obtain many new types of complexiton soliton solution, that is, various combination of trigonometric periodic function and hyperbolic function, various combination of trigonometric periodic function and rational function, various combination of hyperbolic function and rational function solutions.
International Journal of Pure and Apllied Mathematics, 2013
In this article, we use the improved general mapping deformation method based on the generalized ... more In this article, we use the improved general mapping deformation method based on the generalized Jacobi elliptic functions expansion method with computerized symbolic computation to construct some new exact solutions for some nonlinear partial differential equations via the cubic nonlinear Klein-Gordon equation and the modified Kawahara equation. As a result, new generalized Jacobi elliptic function-like solutions are obtained by using this method. This method is more powerful and will be used in further works to establish more entirely new solutions for other kinds of nonlinear partial differential equations arising in mathematical physics when the balance is positive integer and the balance number is not positive integers.
Freezing of paraffin through a channel of air conditioning system was simulated in present study ... more Freezing of paraffin through a channel of air conditioning system was simulated in present study by means of finite volume approach. The sinusoidal air gaps have been imposed within the PCM (phase change material) zone. With inclusion of nanoparticles within RT28, the thermal features have been improved and for estimating the properties, single phase based formulations have been incorporated. The air zone has turbulent regime (Re = 2000 to 3000) and k-ε technique was applied while paraffin zone was laminar. The impact of gravity has been ignored in freezing process and implicit approach for discretization of unsteady terms has been applied. Two levels for fraction of nano-powders and inlet temperature of air have been involved in simulations. The freezing time reduces by 4.58 % with using nanoparticles which is associated with higher conductivity of NEPCM. With reduction of temperature of inlet flow, the solidification time reduces about 27.6 %. With rise of Re from 2e3 to 2.5e3 and 3e3, the freezing rate enhances around 14.3 % and 11.93 %.
An investigation of an axisymmetric mixed convective boundary layer flow of silver-titanium dioxi... more An investigation of an axisymmetric mixed convective boundary layer flow of silver-titanium dioxide/water (Ag−TiO2/H2O) hybrid nanofluid towards vertically and rotating stretching cylinder with entropy generation is conducted. The Cattaneo-Christov theory and joule heating effect are used to analyze the features of thermal energy. Moreover, the magnetic impact and convective boundary conditions on the vertical surface also considered in the current investigation. The developing equations for momentum, energy and entropy generation are modelled and by the usage of similarity variables to transform into the system of nonlinear ordinary differential equations (ODEs). The solutions of nonlinear ODEs are obtained numerically with the assistance of BVP4C MATLAB built-in scheme. The graphical consequences and relevant physical reasoning regarding the velocity, temperature, and concentration profiles are discussed. It is noteworthy that strong estimation of buoyancy ratio and mixed convecti...
This study explores the flow irreversibility of the Ellis hybrid nanofluid (containing CoFe2O4−Ti... more This study explores the flow irreversibility of the Ellis hybrid nanofluid (containing CoFe2O4−TiO2 nanoparticles) with homogeneous and heterogeneous reactions to a horizontal porous stretching cylinder. The energy transportation aspects are investigated in terms of the influence of joule heating and viscous dissipation. The slip and convective boundary conditions are levied on the cylindrical surface, and the mathematical flow model is transferred to a system of nonlinear ordinary differential equations using suitable transformations. The highly nonlinear systems of equations are numerically solved using the bvp4c approach in MATLAB. The graphical outcomes are obtained and discussed; it is worth noting that incremental estimations of the curvature parameter show opposite behaviors on the Ellis fluid velocity and entropy generation, i.e., the entropy generation profile increases while fluid velocity decreases. The boundary layer thinning shows resistance to impact by elasticity and ...
In this paper, the two variables (G G , 1 G)-expansion method is applied to obtain new exact solu... more In this paper, the two variables (G G , 1 G)-expansion method is applied to obtain new exact solutions with parameters of higher-dimensional nonlinear time-fractional differential equations (NTFDEs) in the sense of the conformable fractional derivative. To clarify the veracity of this method, it is implemented in nonlinear (2 + 1)-dimensional time-fractional biological population (BP) model and nonlinear (3 + 1)-dimensional KdV-Zakharov-Kuznetsov (KdV-ZK) equation with time-fractional derivative. When the parameters take some special values, the solitary and periodic solutions are obtained from the hyperbolic and trigonometric function solutions.
Abstract In current study, we use the ( G ′ / G ) -expansion method to construct the closed form ... more Abstract In current study, we use the ( G ′ / G ) -expansion method to construct the closed form solutions of the seventh order time fractional Sawada-Kotera-Ito (TFSKI) equation based on conformable fractional derivative. As a result, trigonometric, hyperbolic and rational functions solutions with arbitrary constants are obtained. When the arbitrary constants are taken some special values, the periodic and soliton solutions are obtained from the travelling wave solutions. The obtained solutions are new and not found elsewhere. The effect of the fractional order on some of these solutions are represented graphically to illustrate the behavior of the exact solutions when the parameter take some special choose.
Abstract The present study is a numerical inspection of the natural convection with double diffus... more Abstract The present study is a numerical inspection of the natural convection with double diffusion in a tilted square cavity filled with a vertical bi-layered composed porous and an adjacent fluid. Isotropic and homogeneous porous layer is considered in this case study. The porous layer is saturated by an aqueous solution with a Prandtl number Pr = 7. The horizontal walls are considered impermeable and adiabatic, while uniform concentrations and temperatures are set on the vertical walls. The Thomas algorithm is employed to find a solution for the system of the governing equations. The divergence of the non-linear system is avoided by introducing under–relaxation factors. The effects of the various non-dimensional governing parameters namely the thickness of porous layer, Rayleigh number, buoyancy ratio, Lewis number, cavity inclination angle, and the thermal conductivity ratio on the thermo-solutal natural convection and the rate of mass and thermal exchange are highlighted and discussed. The predicted findings are given in terms of flow patterns, thermal fields, and iso-concentration lines. The variation of the velocity field, stream function, Sherwood number, and Nusselt number is also inspected. The numerical results show complex flow structure modifying the local transfer (Nusselt and Sherwood numbers).
In this work, bipolar fuzzy parameterized sets in conjunction with soft sets are studied. This r... more In this work, bipolar fuzzy parameterized sets in conjunction with soft sets are studied. This research focuses on the application of bipolar fuzzy parameterized soft sets (BFPSS), arising from association of bipolar fuzzy parameterized sets with soft sets. Some useful operations and fundamental properties of BFPSS are presented. Mainly, we aim to design a novel and comparatively labour-saving algorithm to see the efficacy of BFPSS. We discuss an application of our algorithm in pharmaceutical decision making problem based on effectiveness and harmfulness of certain drugs. However, the algorithm is equally applicable in other decision making environments as well where BFPSS arise. By preserving the structural implication of BFPSS, we compare our technique with a most recent algorithm to prove the significance of our method.
Abstract The vector borne diseases share a high percentage of the annual deaths reported by the w... more Abstract The vector borne diseases share a high percentage of the annual deaths reported by the world health organization. Due to the involvement of multiple factors and resistance of the vector to the treatment strategies, it is highly desired to design a safe, efficient and harmless control strategy. A state of the art computational framework for the Wolbachia induced “genetic-control-strategy” has been documented during this research. The process of mating and molecular identification is complex and expensive and different labs around the world are devoted to format a smooth implementation strategy of this approach. During this research, as a first step, data was collected, secondly, dynamic artificial neural networks, with the “tapped delay” lines are used for nonlinear filtering of the data and for the prediction of the parametric values of the novel mathematical model. To study parametric reliance of stable solutions and unstable solution we analyze stability and the corresponding thresholds desired for this study are documented. The study conducted during this research can prove to be useful in future experimental and theoretical studies, aimed to control the vector borne diseases.
Abstract In the existing numerical analysis is developed to impact of a closed space rectangular ... more Abstract In the existing numerical analysis is developed to impact of a closed space rectangular heat source on natural convective flow-through triangular cavity. The present problem is expressed as non-linear governing equations extended mathematical model is solved by engaging a Galerkin weighted residual process of a finite element scheme. Some investigation is acted for several Rayleigh number (Ra) at Pr = 0.71 on flow pattern and heat variation inside an enclosure. The resulting numerical clarifications of the query are exhibited graphically in phases of streamlines, velocity profiles, isotherms, Rectangular bar effectiveness, mean Nusselt number, and average fluid temperature. The acquired outcomes verified that a rate of heat variation progress with the rise of a Rayleigh number within a triangular cavity. Results are verified relating to a published work.
In the present paper, we construct the traveling wave solutions involving parameters of some nonl... more In the present paper, we construct the traveling wave solutions involving parameters of some nonlinear PDEs in mathematical physics via the nonlinear SchrÖdinger (NLS) equation and the regularized long-wave (RLW) equation by using a simple method which is called the (G'/G)-expansion method, where G=G(ζ) satisfies the second order linear ordinary differential equation. When the parameters are taken special values, the solitary waves are derived from the traveling waves. The traveling wave solutions are expressed by hyperbolic, trigonometric and rational functions. This method is more powerful and will be used in further works to establish more entirely new solutions for other kinds of nonlinear PDEs arising in mathematical physics.
In this paper, the therapeutic interactions are discussed with the aid of a mathematical model an... more In this paper, the therapeutic interactions are discussed with the aid of a mathematical model and piecewise differentiation technique. The model is based on the interaction between cell populations in therapeutic stress and cell populations in neoplastic transformation, referring specifically to triple-negative breast cancer (TNBC). The proposed computational approach provides an opportunity for the qualitative and parametric analysis of the clinical trials in question. The proposed mathematical model is based on the analysis of cell–cell interactions according to a logic that examines pathological stress and its influence on the dynamics of the cell population involved in tumor pathology. Detailed literature review and dynamical analysis of the proposed hypothesis are provided in this paper. The existence and non-negativity of the solutions are exploited, the hypothesis is stabilized; it is then further demonstrated with the aid of the piecewise derivative and the relevant applica...
Abstract This paper retrieves optical solitons to the perturbed Biswas-Milovic equation which des... more Abstract This paper retrieves optical solitons to the perturbed Biswas-Milovic equation which describe the propagation of pulses of various types in optical fiber. Hamiltonian type perturbations are considered with maximum intensity. Kudryashov's law is studied. The Jacobi elliptic function solutions are found using the unified auxiliary equation method. Dark solitons, singular solitons, bright solitons, combo singular solitons and combo dark-singular solitons are obtained.
Abstract This paper studies highly dispersive optical solitons in birefringent fibers with Kerr, ... more Abstract This paper studies highly dispersive optical solitons in birefringent fibers with Kerr, quadratic-cubic, polynomial and non-local laws of refractive index. Three integration schemes adopted are Riccati function approach, sine-Gordon function technique and F -expansion method.
Journal of the Egyptian Mathematical Society, 2017
In this research, we construct the traveling wave solutions for some nonlinear evolution equation... more In this research, we construct the traveling wave solutions for some nonlinear evolution equations in mathematical physics. New solutions such as soliton solutions are found. The method used is the generalized Kudryashov method (GKM). We apply the method successfully to find the exact solutions of the following nonlinear integro-partial differential equations: the (1 + 1)-dimensional integro-differential Ito equation, (2 + 1)-dimensional integro-differential Sawada-Kotera equation and two members of integrodifferential Kadomtsev-Petviashvili (KP) hierarchy equations. These equations have numerous important applications in mathematical physics as well as in engineering. This method is efficient, powerful and simple.
International Journal of Computer Mathematics, 2018
ABSTRACT In this paper, we use the extended trial equation method (ETEM) to construct the exact s... more ABSTRACT In this paper, we use the extended trial equation method (ETEM) to construct the exact solutions in many different functions such as the trigonometric function, elliptic integral function, rational function, hyperbolic function and Jacobi elliptic functions for nonlinear evolution equation in mathematical physics via the fifth-order modified nonlinear Kawahara equation. In this method, the balance number is not constant as we have shown in other methods, but it is changed by changing the trial equation derivative definition. This method is powerful, reliable, effective and simple for solving more complicated nonlinear partial differential equations in mathematical physics.
In this article, we construct the double soliton exact solutions for some nonlinear partial diffe... more In this article, we construct the double soliton exact solutions for some nonlinear partial differential equations in mathematical physics via (2+1)-dimensional Painleve integrable Burgers equations, (2+1)dimensional breaking soliton equations and (2+1)-dimensional Nizhnik-Novikov Veselov equations. We obtain many new types of complexiton soliton solution, that is, various combination of trigonometric periodic function and hyperbolic function, various combination of trigonometric periodic function and rational function, various combination of hyperbolic function and rational function solutions.
International Journal of Pure and Apllied Mathematics, 2013
In this article, we use the improved general mapping deformation method based on the generalized ... more In this article, we use the improved general mapping deformation method based on the generalized Jacobi elliptic functions expansion method with computerized symbolic computation to construct some new exact solutions for some nonlinear partial differential equations via the cubic nonlinear Klein-Gordon equation and the modified Kawahara equation. As a result, new generalized Jacobi elliptic function-like solutions are obtained by using this method. This method is more powerful and will be used in further works to establish more entirely new solutions for other kinds of nonlinear partial differential equations arising in mathematical physics when the balance is positive integer and the balance number is not positive integers.
Freezing of paraffin through a channel of air conditioning system was simulated in present study ... more Freezing of paraffin through a channel of air conditioning system was simulated in present study by means of finite volume approach. The sinusoidal air gaps have been imposed within the PCM (phase change material) zone. With inclusion of nanoparticles within RT28, the thermal features have been improved and for estimating the properties, single phase based formulations have been incorporated. The air zone has turbulent regime (Re = 2000 to 3000) and k-ε technique was applied while paraffin zone was laminar. The impact of gravity has been ignored in freezing process and implicit approach for discretization of unsteady terms has been applied. Two levels for fraction of nano-powders and inlet temperature of air have been involved in simulations. The freezing time reduces by 4.58 % with using nanoparticles which is associated with higher conductivity of NEPCM. With reduction of temperature of inlet flow, the solidification time reduces about 27.6 %. With rise of Re from 2e3 to 2.5e3 and 3e3, the freezing rate enhances around 14.3 % and 11.93 %.
An investigation of an axisymmetric mixed convective boundary layer flow of silver-titanium dioxi... more An investigation of an axisymmetric mixed convective boundary layer flow of silver-titanium dioxide/water (Ag−TiO2/H2O) hybrid nanofluid towards vertically and rotating stretching cylinder with entropy generation is conducted. The Cattaneo-Christov theory and joule heating effect are used to analyze the features of thermal energy. Moreover, the magnetic impact and convective boundary conditions on the vertical surface also considered in the current investigation. The developing equations for momentum, energy and entropy generation are modelled and by the usage of similarity variables to transform into the system of nonlinear ordinary differential equations (ODEs). The solutions of nonlinear ODEs are obtained numerically with the assistance of BVP4C MATLAB built-in scheme. The graphical consequences and relevant physical reasoning regarding the velocity, temperature, and concentration profiles are discussed. It is noteworthy that strong estimation of buoyancy ratio and mixed convecti...
This study explores the flow irreversibility of the Ellis hybrid nanofluid (containing CoFe2O4−Ti... more This study explores the flow irreversibility of the Ellis hybrid nanofluid (containing CoFe2O4−TiO2 nanoparticles) with homogeneous and heterogeneous reactions to a horizontal porous stretching cylinder. The energy transportation aspects are investigated in terms of the influence of joule heating and viscous dissipation. The slip and convective boundary conditions are levied on the cylindrical surface, and the mathematical flow model is transferred to a system of nonlinear ordinary differential equations using suitable transformations. The highly nonlinear systems of equations are numerically solved using the bvp4c approach in MATLAB. The graphical outcomes are obtained and discussed; it is worth noting that incremental estimations of the curvature parameter show opposite behaviors on the Ellis fluid velocity and entropy generation, i.e., the entropy generation profile increases while fluid velocity decreases. The boundary layer thinning shows resistance to impact by elasticity and ...
In this paper, the two variables (G G , 1 G)-expansion method is applied to obtain new exact solu... more In this paper, the two variables (G G , 1 G)-expansion method is applied to obtain new exact solutions with parameters of higher-dimensional nonlinear time-fractional differential equations (NTFDEs) in the sense of the conformable fractional derivative. To clarify the veracity of this method, it is implemented in nonlinear (2 + 1)-dimensional time-fractional biological population (BP) model and nonlinear (3 + 1)-dimensional KdV-Zakharov-Kuznetsov (KdV-ZK) equation with time-fractional derivative. When the parameters take some special values, the solitary and periodic solutions are obtained from the hyperbolic and trigonometric function solutions.
Abstract In current study, we use the ( G ′ / G ) -expansion method to construct the closed form ... more Abstract In current study, we use the ( G ′ / G ) -expansion method to construct the closed form solutions of the seventh order time fractional Sawada-Kotera-Ito (TFSKI) equation based on conformable fractional derivative. As a result, trigonometric, hyperbolic and rational functions solutions with arbitrary constants are obtained. When the arbitrary constants are taken some special values, the periodic and soliton solutions are obtained from the travelling wave solutions. The obtained solutions are new and not found elsewhere. The effect of the fractional order on some of these solutions are represented graphically to illustrate the behavior of the exact solutions when the parameter take some special choose.
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Papers by Khaled Gepreel