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EFFECT OF PERTURBATION IN THE SOLUTION OF FRACTIONAL NEUTRAL FUNCTIONAL DIFFERENTIAL EQUATIONS
MOHAMMED. S. ABDO,SATISH. K. PANCHAL 한국산업응용수학회 2018 Journal of the Korean Society for Industrial and A Vol.22 No.1
In this paper, we study the initial value problem for neutral functional differential equations involving Caputo fractional derivative of order α ∈ (0, 1) with infinite delay. Some sufficient conditions for the uniqueness and continuous dependence of solutions are established by virtue of fractional calculus and Banach fixed point theorem. Some results obtained showed that the solution was closely related to the conditions of delays and minor changes in the problem. An example is provided to illustrate the main results.
Nonlinear implicit fractional differential equation involving -Caputo fractional derivative
MOHAMMED S. ABDO,AHMED G. IBRAHIM,SATISH K. PANCHAL 장전수학회 2019 Proceedings of the Jangjeon mathematical society Vol.22 No.3
In this paper, we consider a nonlinear implicit fractional dierential equation with nonlocal condition and involving the Caputo fractional derivative with respect to another function. We investigate the existence, uniqueness of solution on subinterval of the original interval. Hence we give an estimation for this solution. Further, we discuss the continuous dependence of solution involved in the problem. The results obtained by means of a variety of tools fractional calculus including Banach contraction mapping principle. Illustrative examples are also given.
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.
EXISTENCE AND UNIQUENESS RESULTS FOR CAPUTO FRACTIONAL INTEGRO-DIFFERENTIAL EQUATIONS
AHMED A. HAMOUD,MOHAMMED. S. ABDO,KIRTIWANT P. GHADLE 한국산업응용수학회 2018 Journal of the Korean Society for Industrial and A Vol.22 No.3
This paper successfully applies the modified Adomian decomposition method to find the approximate solutions of the Caputo fractional integro-differential equations. The reliability of the method and reduction in the size of the computational work give this method a wider applicability. Also,the behavior of the solution can be formally determined by analytical approximation. Moreover, we proved the existence and uniqueness results and convergence of the solution. Finally,an example is included to demonstrate the validity and applicability of the proposed technique.