Papers by Abdellah Taqbibt
Boletim da Sociedade Paranaense de Matemática, May 21, 2024
DergiPark (Istanbul University), Feb 2, 2023
In this paper, by using the fixed point results of α-φ-Geraghty type mappings, the existence and ... more In this paper, by using the fixed point results of α-φ-Geraghty type mappings, the existence and uniqueness results for solutions to differential equations involving the generalized Caputo-Fabrizio derivative are investigated in λ-metric spaces. As application, an illustrative example is given to show the applicability of our theoretical results.
AIMS Mathematics
This paper aims to introduce the new concept of an $ \alpha $-$ \theta $-Geraghty type contractio... more This paper aims to introduce the new concept of an $ \alpha $-$ \theta $-Geraghty type contraction mapping using $ \mathcal{C}_{\mathcal{G}} $-simulation in a metric-like space. Additionally, through this type of contraction, we establish fixed point results that generalize several known fixed point results in the literature. We provide some examples as an application that proves the credibility of our results.
Journal of Mathematical Sciences
The paper is devoted to proving an existence and uniqueness result for generalized solution to a ... more The paper is devoted to proving an existence and uniqueness result for generalized solution to a class of nonlinear wave equations in space dimensions d = 1, 2, 3. It is shown that for a nonlinearity of f and arbitrary growth and sign, which depends on the time variable and parameter, the initial value problem for the linear wave equation has a unique solution in a Colombeau subalgebra of bounded type. The proof is based on a fixed point theorem in an ultrametric topology on a closed subspace of these subalgebras. The results presented generalize and unify several existing results in the literature.
The aim of this work is to provide the existence and uniqueness of a fixed point for a new SF -GF... more The aim of this work is to provide the existence and uniqueness of a fixed point for a new SF -GF -contraction type. We show its properties, we also generalize and unify several results in the literature . Finally, we give some examples and applications to describe these results. Mathematics Subject Classification (2010). 34A08, 26A33,34K37.
Journal of Linear and Topological Algebra, 2019
The present paper is devoted to the existence and uniqueness result of the fractional evolution ... more The present paper is devoted to the existence and uniqueness result of the fractional evolution equation $D^{q}_c u(t)=g(t,u(t))=Au(t)+f(t)$ for the real $qin (0,1)$ with the initial value $u(0)=u_{0}intilde{R}$, where $tilde{R}$ is the set of all generalized real numbers and $A$ is an operator defined from $mathcal G$ into itself. Here the Caputo fractional derivative $D^{q}_c$ is used instead of the usual derivative. The introduction of locally convex spaces is to use their topology in order to define generalized semigroups and generalized fixed points, then to show our requested result.
In the present article, we investigate a new concept of fixedpoint theorems in the framework of C... more In the present article, we investigate a new concept of fixedpoint theorems in the framework of Colombeau algebra of gen-eralized funtions. introduce a characterisation of the continuity of some C−linear maps, We gave another representation of the contraction of the maps among Colombian algebras.In addition, wehave given a general frame of fixed-point theorems in the clas-sic: the fixed point theorems of Banach, Kannan and Chatterjea.We concluded the applicability of these results by an application.
2020 IEEE 6th International Conference on Optimization and Applications (ICOA), 2020
This paper is concerning to the generalized heat eqution result, but this time by using the notio... more This paper is concerning to the generalized heat eqution result, but this time by using the notion of generalized fixed point.We introduce the Gronwall's inequality in order to prove the uniqueness of the solution
2021 7th International Conference on Optimization and Applications (ICOA)
The present paper is devoted to discuss the existence and uniqueness of the fuzzy fractional boun... more The present paper is devoted to discuss the existence and uniqueness of the fuzzy fractional boundary problem. The main tools employed is fixed point of Banach. we give some examples in order to illustrate the situations.
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Papers by Abdellah Taqbibt