Numerical solution of stochastic fractional integro-differential/ Itô-Volterra integral equations via fractional Genocchi wavelets

Articles in Press

Document Type : Research Paper

Authors

1 Faculty of Science, Mahallat Institute of Higher Education, Mahallat, Iran.

2 Department of Mathematics, Faculty of Mathematical Sciences, Alzahra University, Tehran, Iran.

3 Centro de Matemática Computacional e Estocástica, Instituto Superior Técnico, Universidade de Lisboa, Portugal.

Abstract

In this research, a novel approach based on the fractional-order Genocchi wavelets (FGWs),
inverse hyperbolic functions, and collocation technique is introduced for obtaining numerical
solutions of stochastic fractional integro-differential equations (SFIDEs) and Itô-Volterra integral equations (IVIEs). Initially, we utilize the Laplace transform approach to approximate
the Caputo fractional derivative. Then, the unknown solution is approximated via combination of the FGWs and inverse hyperbolic functions. We replace this approximation and
its derivatives into the resulting stochastic equation (SE). By the Gauss-Legendre quadrature
rule (GLQR) and collocation method, we achieve a system of nonlinear algebraic equations.
The derived algebraic system can be readily solved through application of Newton’s iterative
scheme. Also, we show the convergence of the mentioned scheme. Ultimately, several test
problems are examined to demonstrate the applicability and effectiveness of the suggested
technique.

Keywords

Main Subjects

Computational Methods for Differential Equations

Articles in Press, Accepted Manuscript
Available Online from 26 January 2025

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History

  • Receive Date: 24 October 2024
  • Revise Date: 14 December 2024
  • Accept Date: 20 January 2025

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