Numerical Approaches for Solving Mixed Volterra-Fredholm Fractional Integro-Differential Equations

DOI

10.2991/978-94-6463-014-5_26How to use a DOI?

Keywords

Fractional integro-differential equation; Caputo derivatives; Adomian polynomial; Residual function

Abstract

In this paper, an approximate solution for solving nonlinear mixed Volterra-Fredholm fractional integro-differential equations is presented. The fractional derivative is defined in terms of Caputo type. Two methods are suggested: Adomin Decomposition Method (ADM) and Residual Power Series Method (RPSM). In these methods, Adomian polynomials and residual function are derived. The fractional Volterra-Fredholm integro-differential equation is reduced to a recurrence formula, in which it can be solved rather straightforward. Numerical examples demonstrate the efficiency and accuracy of ADM over RPSM.

Copyright

© 2023 The Author(s)

Open Access

Open Access This chapter is licensed under the terms of the Creative Commons Attribution-NonCommercial 4.0 International License (http://creativecommons.org/licenses/by-nc/4.0/), which permits any noncommercial use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license and indicate if changes were made.

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TY  - CONF
AU  - N. M. A. Nik Long
AU  - K. Alsa’di
PY  - 2022
DA  - 2022/12/12
TI  - Numerical Approaches for Solving Mixed Volterra-Fredholm Fractional Integro-Differential Equations
BT  - Proceedings of the International Conference on Mathematical Sciences and Statistics 2022 (ICMSS 2022)
PB  - Atlantis Press
SP  - 278
EP  - 285
SN  - 2352-538X
UR  - https://doi.org/10.2991/978-94-6463-014-5_26
DO  - 10.2991/978-94-6463-014-5_26
ID  - Long2022
ER  -