APPROXIMATE SOLUTION FOR MULTI-HIGHER NONLINEARFRACTIONAL VOLTERRA- FREDHLOM INTEGRO-DIFFERENTIALEQUATIONS

In this paper finds semi-approximate solutions for nonlinear Integro-Differen-tial Equations of fractional order (FIDEs) of the Volterra-Fredholm-Hammerstein (VF-H) type, where the higher-order fractional derivative is defined in the Caputo sense, by effectively using the Adomian Decomposition Metho...

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Published inTWMS journal of applied and engineering mathematics Vol. 15; no. 8; p. 1963
Main Authors Hamood, M.M, Sharif, A.A, Ghadle, K.P
Format Journal Article
LanguageEnglish
Published Turkic World Mathematical Society 01.08.2025
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Yemen
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Summary:In this paper finds semi-approximate solutions for nonlinear Integro-Differen-tial Equations of fractional order (FIDEs) of the Volterra-Fredholm-Hammerstein (VF-H) type, where the higher-order fractional derivative is defined in the Caputo sense, by effectively using the Adomian Decomposition Method and the Modified Adomian Decomposition Method as computational techniques. This method involves converting VF-H type FIDEs into iterative algebraic equations. In this approach, the answer to these equations is the product of an endless series of terms, which usually converges to the solution given by the noise terms. For numerical reasons, a reduced number of terms is utilised when a closed-form solution cannot be found. Lastly, these notions are illustrated using examples. Keywords: Volterra-Fredholm-Hammerstein, Caputo-fractional derivative, Adomian decomposition method, Modified Adomian decomposition method. AMS Subject Classification: 34A08, 26A33, 37C25.
ISSN:2146-1147