Browsing by Author "Laadjal, Zaid"

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Citation - WoS: 3
Citation - Scopus: 3
Analysis of a Coupled System of Nonlinear Fractional Langevin Equations with Certain Nonlocal and Nonseparated Boundary Conditions
(Hindawi Ltd, 2021) Laadjal, Zaid; Jarad, Fahd; Al-Mdallal, Qasem M.; Jarad, Fahd; 234808
In this article, we use some fixed point theorems to discuss the existence and uniqueness of solutions to a coupled system of a nonlinear Langevin differential equation which involves Caputo fractional derivatives of different orders and is governed by new type of nonlocal and nonseparated boundary conditions consisting of fractional integrals and derivatives. The considered boundary conditions are totally dissimilar than the ones already handled in the literature. Additionally, we modify the Adams-type predictor-corrector method by implicitly implementing the Gauss-Seidel method in order to solve some specific particular cases of the system.
Citation - WoS: 10
Citation - Scopus: 12
Existence, uniqueness and stability of solutions for generalized proportional fractional hybrid integro-differential equations with Dirichlet boundary conditions
(Amer inst Mathematical Sciences-aims, 2022) Laadjal, Zaid; Jarad, Fahd; Jarad, Fahd; 234808
In this work, the existence of solutions for nonlinear hybrid fractional integro-differential equations involving generalized proportional fractional (GPF) derivative of Caputo-Liouville-type and multi-term of GPF integrals of Reimann-Liouville type with Dirichlet boundary conditions is investigated. The analysis is accomplished with the aid of the Dhage's fixed point theorem with three operators and the lower regularized incomplete gamma function. Further, the uniqueness of solutions and their Ulam-Hyers-Rassias stability to a special case of the suggested hybrid problem are discussed. For the sake of corroborating the obtained results, an illustrative example is presented.
Citation - WoS: 6
Citation - Scopus: 8
On a langevin equation involving caputo fractional proportional derivatives with respect to another function
(Amer inst Mathematical Sciences-aims, 2022) Laadjal, Zaid; Jarad, Fahd; Jarad, Fahd; 234808
In this work, we introduce and study a class of Langevin equation with nonlocal boundary conditions governed by a Caputo fractional order proportional derivatives of an unknown function with respect to another function. The qualitative results concerning the given problem are obtained with the aid of the lower regularized incomplete Gamma function and applying the standard fixed point theorems. In order to homologate the theoretical results we obtained, we present two examples.
Citation - WoS: 12
Citation - Scopus: 16
On existence–uniqueness results for proportional fractional differential equations and incomplete gamma functions
(Springer, 2020) Abdeljawad, Thabet; Laadjal, Zaid; Abdeljawad, Thabet; Jarad, Fahd; Jarad, Fahd; 234808
In this article, we employ the lower regularized incomplete gamma functions to demonstrate the existence and uniqueness of solutions for fractional differential equations involving nonlocal fractional derivatives (GPF derivatives) generated by proportional derivatives of the form D-rho=(1-rho)+rho D, rho is an element of[0,1], (1) where D is the ordinary differential operator.
Citation - WoS: 4
Citation - Scopus: 3
Sharp estimates of the unique solution for two-point fractional boundary value problems with conformable derivative
(Wiley, 2024) Abdeljawad, Thabet; Laadjal, Zaid; Abdeljawad, Thabet; Jarad, Fahd; Jarad, Fahd; 234808
In this work, we investigate the condition of the given interval which ensures the existence and uniqueness of solutions for two-point boundary value problems within conformable-type local fractional derivative. The method of analysis is obtained by the principle of contraction mapping. Furthermore, benefiting from calculating the integral of the Green's function, we are able to improve a recent result by obtaining a sharper lower bound for an eigenvalue problem. Two examples are presented to clarify the obtained results. Finally, we present an open problem for the interested reader.
Citation - WoS: 1
Citation - Scopus: 2
Some results for two classes of two-point local fractional proportional boundary value problems
(Univ Nis, Fac Sci Math, 2023) Abdeljawad, Thabet; Laadjal, Zaid; Abdeljawad, Thabet; Jarad, Fahd; Jarad, Fahd; 234808
In this paper, we consider two classes of boundary value problems in the frame of local proportional fractional derivatives. For both of these classes, we obtain the associated Green's functions and discuss their properties. Using these properties, we go about the uniqueness of the solutions. In addition, we establish Lyapunov-type and Hartman-Wintner-type inequalities and build sharp estimated for the unique solutions of the considered equations.