Papers by Muhammad Samraiz
Fractional Differential Calculus, 2019
In this article we establish the variant of Hardy-type and refined Hardy-type inequalities for a ... more In this article we establish the variant of Hardy-type and refined Hardy-type inequalities for a generalized Riemann-Liouville fractional integral operator and Riemann-Liouville k-fractional integral operator using convex and monotone convex functions. We also discuss one dimensional cases of our related results. As special cases of our general results we obtain the consequences of Iqbal et al. [11]. We also obtained exponentially convex linear functionals for the generalized fractional integral operators. Moreover, it includes Cauchy means for the above mentioned operators.
Fractal and Fractional
The significance of fractional calculus cannot be underestimated, as it plays a crucial role in t... more The significance of fractional calculus cannot be underestimated, as it plays a crucial role in the theory of inequalities. In this paper, we study a new class of mean-type inequalities by incorporating Riemann-type fractional integrals. By doing so, we discover a novel set of such inequalities and analyze them using different mathematical identities. This particular class of inequalities is introduced by employing a generalized convexity concept. To validate our work, we create visual graphs and a table of values using specific functions to represent the inequalities. This approach allows us to demonstrate the validity of our findings and further solidify our conclusions. Moreover, we find that some previously published results emerge as special consequences of our main findings. This research serves as a catalyst for future investigations, encouraging researchers to explore more comprehensive outcomes by using generalized fractional operators and expanding the concept of convexity.
Fractal and fractional, Apr 22, 2023
Symmetry
Convexity performs the appropriate role in the theoretical study of inequalities according to the... more Convexity performs the appropriate role in the theoretical study of inequalities according to the nature and behavior. Its significance is raised by the strong connection between symmetry and convexity. In this article, we consider a new parameterized quantum fractional integral identity. By applying this identity, we obtain as main results some integral inequalities of trapezium, midpoint and Simpson’s type pertaining to s-convex functions. Moreover, we deduce several special cases, which are discussed in detail. To validate our theoretical findings, an example and application to special means of positive real numbers are presented. Numerical analysis investigation shows that the mixed fractional calculus with quantum calculus give better estimates compared with fractional calculus or quantum calculus separately.
Journal of Inequalities and Applications
In this article, we introduce a class of functions $\mathfrak{U}(\mathfrak{p})$ U ( p ) with inte... more In this article, we introduce a class of functions $\mathfrak{U}(\mathfrak{p})$ U ( p ) with integral representation defined over a measure space with σ-finite measure. The main purpose of this paper is to extend the Minkowski and related inequalities by considering general kernels. As a consequence of our general results, we connect our results with various variants for the fractional integrals operators. Such applications have wide use and importance in the field of applied sciences.
Computer Modeling in Engineering & Sciences
In this paper, we establish the new forms of Riemann-type fractional integral and derivative oper... more In this paper, we establish the new forms of Riemann-type fractional integral and derivative operators. The novel fractional integral operator is proved to be bounded in Lebesgue space and some classical fractional integral and differential operators are obtained as special cases. The properties of new operators like semi-group, inverse and certain others are discussed and its weighted Laplace transform is evaluated. Fractional integro-differential freeelectron laser (FEL) and kinetic equations are established. The solutions to these new equations are obtained by using the modified weighted Laplace transform. The Cauchy problem and a growth model are designed as applications along with graphical representation. Finally, the conclusion section indicates future directions to the readers.
Symmetry
In this article, we provide constraints for the sum by employing a generalized modified form of f... more In this article, we provide constraints for the sum by employing a generalized modified form of fractional integrals of Riemann-type via convex functions. The mean fractional inequalities for functions with convex absolute value derivatives are discovered. Hermite–Hadamard-type fractional inequalities for a symmetric convex function are explored. These results are achieved using a fresh and innovative methodology for the modified form of generalized fractional integrals. Some applications for the results explored in the paper are briefly reviewed.
arXiv: Mathematical Physics, 2012
In this paper, the iterative method developed by Daftardar-Gejji and Jafari (DJ method) is employ... more In this paper, the iterative method developed by Daftardar-Gejji and Jafari (DJ method) is employed for analytic treatment of Laplace equation with Dirichlet and Neumann boundary conditions. The method is demonstrated by several physical models of Laplace equation. The obtained results show that the present approach is highly accurate and requires reduced amount of calculations compared with the existing iterative methods.
Results in Physics, 2013
In this paper, the iterative method developed by Daftardar-Gejji and Jafari (DJ method) is employ... more In this paper, the iterative method developed by Daftardar-Gejji and Jafari (DJ method) is employed for analytic treatment of Laplace equation with Dirichlet and Neumann boundary conditions. The method is demonstrated by several physical models of Laplace equation. The obtained results show that the present approach is highly accurate and requires reduced amount of calculations compared with the existing iterative methods.
Symmetry
This study deals with a novel class of mean-type inequalities by employing fractional calculus an... more This study deals with a novel class of mean-type inequalities by employing fractional calculus and convexity theory. The high correlation between symmetry and convexity increases its significance. In this paper, we first establish an identity that is crucial in investigating fractional mean inequalities. Then, we establish the main results involving the error estimation of the Hermite–Hadamard inequality for composite convex functions via a generalized Riemann-type fractional integral. Such results are verified by choosing certain composite functions. These results give well-known examples in special cases. The main consequences can generalize many known inequalities that exist in other studies.
Mathematics
In this paper, the authors established several new inequalities of the Beesack–Wirtinger type for... more In this paper, the authors established several new inequalities of the Beesack–Wirtinger type for different kinds of differentiable convex functions. Furthermore, we generalized our results for functions that are n-times differentiable convex. Finally, many interesting Ostrowski- and Chebyshev-type inequalities are given as well.
AIMS Mathematics
In this paper, we prove several new integral inequalities for the $ k $-Hilfer fractional derivat... more In this paper, we prove several new integral inequalities for the $ k $-Hilfer fractional derivative operator, which is a fractional calculus operator. As a result, we have a whole new set of fractional integral inequalities. For the generalized fractional derivative, we also use Young's inequality to find new forms of inequalities. Such conclusions for this novel and generalized fractional derivative are extremely useful and valuable in the domains of differential equations and fractional differential calculus, both of which have a strong connections to real-world situations. These findings may stimulate additional research in a variety of fields of pure and applied sciences.
Fractal and Fractional
In the recent era of research, the field of integral inequalities has earned more recognition due... more In the recent era of research, the field of integral inequalities has earned more recognition due to its wide applications in diverse domains. The researchers have widely studied the integral inequalities by utilizing different approaches. In this present article, we aim to develop a variety of certain new inequalities using the generalized fractional integral in the sense of multivariate Mittag-Leffler (M-L) functions, including Grüss-type and some other related inequalities. Also, we use the relationship between the Riemann-Liouville integral, the Prabhakar integral, and the generalized fractional integral to deduce specific findings. Moreover, we support our findings by presenting examples and corollaries.
Fractal and Fractional
The Hermite-Hadamard inequalities for κ-Riemann-Liouville fractional integrals (R-LFI) are presen... more The Hermite-Hadamard inequalities for κ-Riemann-Liouville fractional integrals (R-LFI) are presented in this study using a relatively novel approach based on Abel-Gontscharoff Green’s function. In this new technique, we first established some integral identities. Such identities are used to obtain new results for monotonic functions whose second derivative is convex (concave) in absolute value. Some previously published inequalities are obtained as special cases of our main results. Various applications of our main consequences are also explored to special means and trapezoid-type formulae.
In this article, we introduce a class of functions U(p) with integral representation defined over... more In this article, we introduce a class of functions U(p) with integral representation defined over measure space with σ-finite measure. The main purpose of this paper is to extend the Minkowski and related inequalities by considering general kernels. As a consequence of our general results, we connect our results with various variants for the fractional integrals operators. Such applications have wide use and importance in the field of applied sciences.AMS Subject Classification: 26D15; 26D10; 26A33; 34B27
AIMS Mathematics
In this paper, a new class of Hermite-Hadamard type integral inequalities using a strong type of ... more In this paper, a new class of Hermite-Hadamard type integral inequalities using a strong type of convexity, known as $ n $-polynomial exponential type $ s $-convex function, is studied. This class is established by utilizing the Hölder's inequality, which has several applications in optimization theory. Some existing results of the literature are obtained from newly explored consequences. Finally, some novel limits for specific means of positive real numbers are shown as applications.
AIMS mathematics, 2022
In this paper, we describe generalized fractional integral operator and its inverse with generali... more In this paper, we describe generalized fractional integral operator and its inverse with generalized Bessel-Maitland function (BMF-V) as its kernel. We discuss its convergence, boundedness, its relation with other well known fractional operators (Saigo fractional integral operator , Riemann-Liouville fractional operator), and establish its integral transform. Moreover, we have given the relationship of BMF-V with Mittag-Leffler functions.
Symmetry, 2022
In this paper, we give some correct quantum type Simpson’s inequalities via the application of q-... more In this paper, we give some correct quantum type Simpson’s inequalities via the application of q-Hölder’s inequality. The inequalities of this study are compatible with famous Simpson’s 1/8 and 3/8 quadrature rules for four and six panels, respectively. Several special cases from our results are discussed in detail. A counter example is presented to explain the limitation of Hölder’s inequality in the quantum framework.
Advances in Difference Equations, 2020
It is always attractive and motivating to acquire the generalizations of known results. In this a... more It is always attractive and motivating to acquire the generalizations of known results. In this article, we introduce a new class$\mathfrak{C(h)}$C(h)of functions which can be represented in a form of integral transforms involving general kernel withσ-finite measure. We obtain some new Pólya–Szegö and Čebyšev type inequalities as generalizations to the previously proved ones for different fractional integrals including fractional integral of a function with respect to another function capturing Riemann–Liouville integrals, Hadamard fractional integrals, Katugampola fractional integral operators, and conformable fractional integrals. This new idea shall motivate the researchers to prove the results over a measure space with general kernels instead of special kernels.
Frontiers in Physics, 2020
In this paper we introduce the (k, s)-Hilfer-Prabhakar fractional derivative and discuss its prop... more In this paper we introduce the (k, s)-Hilfer-Prabhakar fractional derivative and discuss its properties. We find the generalized Laplace transform of this newly proposed operator. As an application, we develop the generalized fractional model of the free-electron laser equation, the generalized time-fractional heat equation, and the generalized fractional kinetic equation using the (k, s)-Hilfer-Prabhakar derivative.
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Papers by Muhammad Samraiz