Solving Linear and Nonlinear Fuzzy Fractional Volterra-Fredholm Integro Differential Equations Using Shehu Adomian Decomposition Method

S Luvis Savla; R Gethsi Sharmila

doi:10.17485/IJST/v17i12.156

Article

Solving Linear and Nonlinear Fuzzy Fractional Volterra-Fredholm Integro Differential Equations Using Shehu Adomian Decomposition Method

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Indian Journal of Science and Technology

DOI: 10.17485/IJST/v17i12.156

Year: 2024, Volume: 17, Issue: 12, Pages: 1222-1230

Original Article

Solving Linear and Nonlinear Fuzzy Fractional Volterra-Fredholm Integro Differential Equations Using Shehu Adomian Decomposition Method

S Luvis Savla¹, R Gethsi Sharmila^2*

¹Research Scholar, PG & Research Department of Mathematics, Bishop Heber College (affiliated to Bharathidasan University), Tiruchirapppalli-17, Tamil Nadu, India
²Associate Professor, PG & Research Department of Mathematics, Bishop Heber College (affiliated to Bharathidasan University), Tiruchirapppalli-17, Tamil Nadu, India

*Corresponding Author
Email: [email protected]

Received Date:20 January 2024, Accepted Date:29 January 2024, Published Date:20 March 2024

This work is licensed under a Creative Commons Attribution 4.0 International License.

Abstract

Objectives: In applied sciences and engineering, fuzzy fractional differential equations (FFDEs) and fuzzy fractional integral equations (FFIEs) are a crucial topic. The main objective of this work is to discover an analytical approximate solution for the fuzzy fractional Volterra-Fredholm integro differential equations (FFVFIDE). In the Caputo concept, fractional derivatives are regarded. Methods: The Shehu transform is challenging to exist for nonlinear problems. So, the Shehu transform is combined with the Adomian decomposition method is called the Shehu Adomian decomposition method (SHADM) and has been proposed to solve both linear and nonlinear FFVFIDEs. Findings: Both linear and nonlinear FFVIFIDEs can be solved using this technique. For nonlinear terms, Adomian polynomials have been used. The main benefit of this approach is that it converges quickly to the exact solution. Figures and numerical examples demonstrate the expertise of the suggested approach. Novelty: The comparison between the exact solution and numerical solution is shown in figures for various values of fractional order . The numerical evolution demonstrates the efficiency and reliability of the proposed SHADM. The proposed approach is rapid, exact, and simple to apply and produce excellent outcomes.

Keywords: Fractional calculus, fuzzy number, Mittag Leffler function, Shehu Adomian decomposition method, fuzzy fractional Volterra-Fredholm integro differential equation

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Copyright

© 2024 Savla & Sharmila. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Published By Indian Society for Education and Environment (iSee)