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Ahmed A. Hamoud,Nedal M. Mohammed,Homan Emadifar,Faraidum K. Hamasalh,Soubhagya Kumar Sahoo,Masoumeh Khademi,Foroud Parvaneh 한국지능시스템학회 2022 INTERNATIONAL JOURNAL of FUZZY LOGIC and INTELLIGE Vol.22 No.4
In this paper, we established some new results concerning the existence and uniquenessof the solutions of nonlinear Atangana-Baleanu-Caputo fractional (ABC-fractional) FuzzyVolterra-Fredholm integro-differential equations. These new findings are obtained using thetheorems of a fixed point. In addition, we investigate Hyers-Ulam stability for this fractionalsystem. Our work extends and improves the results in the literature. Finally, some examplesdemonstrate the validity of the obtained theoretical results.
SOLVING FREDHOLM INTEGRO-DIFFERENTIAL EQUATIONS BY USING NUMERICAL TECHNIQUES
Hamoud Ahmed A.,Hussain Khawlah H.,Mohammed Nedal M.,Ghadle Kirtiwant P. 경남대학교 수학교육과 2019 Nonlinear Functional Analysis and Applications Vol.24 No.3
This paper mainly focuses on numerical techniques based on the Adomian Decomposition Method (ADM) and Direct Homotopy Analysis Method (DHAM) for solving Fredholm integro-differential equations of the second kind. The reliability of the methods and reduction in the size of the computational work give this methods wider applicability. Convergence analysis of the exact solution of the proposed methods will be established. Moreover, we proved the uniqueness of the solution. To illustrate the methods, an example is presented.
SOME NEW UNIQUENESS RESULTS FOR FRACTIONAL INTEGRO-DIFFERENTIAL EQUATIONS
Hussain Khawlah H.,Hamoud Ahmed A.,Mohammed Nedal M. 경남대학교 수학교육과 2019 Nonlinear Functional Analysis and Applications Vol.24 No.4
The main objective of this paper is to investigate and prove the existence and uniqueness theorems of the solution of nonlinear Volterra-Fredholm integro-differential equations of fractional order. The theorems of two types for the nonlinear fractional order Volterra-Fredholm integro-di erential equations such as one- and two-dimensional are proved by applying the fixed point theorem of Banach space couple with contraction mapping principle, in which the su cient conditions are presented in order to ensure the existence and uniqueness of a unique xed point related to the Volterra-Fredholm integro-di erential equation in operator form.