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Mohammed N. Alkord,Sadikali L. Shaikh,Saleh S. Redhwan,Mohammed S. Abdo 경남대학교 수학교육과 2023 Nonlinear Functional Analysis and Applications Vol.28 No.2
In this paper, we consider two types of fractional boundary value problems, one of them is an implicit type and the other will be an integro-differential type with nonlocal integral multi-point boundary conditions in the frame of generalized Hilfer fractional derivatives. The existence and uniqueness results are acquired by applying Krasnoselskii’s and Banach’s fixed point theorems. Some various numerical examples are provided to illustrate and validate our results. Moreover, we get some results in the literature as a special case of our current results.
ANALYTICAL AND APPROXIMATE SOLUTIONS FOR GENERALIZED FRACTIONAL QUADRATIC INTEGRAL EQUATION
Basim N. Abood,Saleh S. Redhwan,Mohammed S. Abdo 경남대학교 수학교육과 2021 Nonlinear Functional Analysis and Applications Vol.26 No.3
In this paper, we study the analyticaland approximate solutions for a fractional quadratic integral equationinvolving Katugampola fractional integral operator. The existence anduniqueness results obtained in the given arrangement are not only new butalso yield some new particular results corresponding to special values ofthe parameters $\rho $ and $\vartheta $. The main results are obtained byusing Banach fixed point theorem, Picard Method, and Adomian decompositionmethod. An illustrative example is given to justify the main results.
CAPUTO DELAYED FRACTIONAL DIFFERENTIAL EQUATIONS BY SADIK TRANSFORM
Awad T. Alabdala,Basim N. Abood,Saleh S. Redhwan,Soliman Alkhatib 경남대학교 수학교육과 2023 Nonlinear Functional Analysis and Applications Vol.28 No.2
In this article, we are interested in studying the fractional Sadik Transform and a combination of the method of steps that will be applied together to find accurate solutions or approximations to homogeneous and non-homogeneous delayed fractional differential equations with constant-coefficient and possible extension to time-dependent delays. The results show that the process is correct, exact, and easy to do for solving delayed fractional differential equations near the origin. Finally, we provide several examples to illustrate the applicability of this method.
Awad T. Alabdala,Alan jalal abdulqader,Saleh S. Redhwan,Tariq A. Aljaaidi 경남대학교 수학교육과 2023 Nonlinear Functional Analysis and Applications Vol.28 No.4
In this paper, we are motivatedto evaluate and investigate the necessary conditions for the fractionalVolterra Fredholm integro-differential equation involving the $\varsigma $%-Hilfer fractional derivative. The given problem is converted into anequivalent fixed point problem by introducing an operator whose fixed points coincide with the solutions to the problem at hand. The existence anduniqueness results for the given problem are derived by applyingKrasnoselskii and Banach fixed point theorems respectively. Furthermore, weinvestigate the convergence of approximated solutions to the same problem using the modified Adomian decomposition method. An example is provided to illustrate our findings.