10.1007/s40096-023-00514-3

Hahn wavelets collocation method combined with Laplace transform method for solving fractional integro-differential equations

  • P. Rahimkhani1,
  • Y. Ordokhani*2,
  1. Faculty of Science, Mahallat Institute of Higher Education, Mahallat, IR
  2. Department of Mathematics, Faculty of Mathematical Sciences, Alzahra University, Tehran, IR

Published in Issue 2023-03-30

How to Cite

Rahimkhani, P., & Ordokhani, Y. (2023). Hahn wavelets collocation method combined with Laplace transform method for solving fractional integro-differential equations. Mathematical Sciences, 18(3 (September 2024). https://doi.org/10.1007/s40096-023-00514-3
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Abstract

Abstract The main idea of this paper is to establish the novel Hahn wavelets for solving fractional-order integro-differential equations (FIDEs). First, we introduce Hahn wavelets and some of their properties. Then, we convert FIDEs into integer-order integro-differential equations (IIDEs) using the Laplace transform method. Finally, the yielded IIDEs using the Hahn wavelets, activation functions, the Legendre–Gauss quadrature formula and collocation method transformed to a system of algebraic equations which can be easily solved by applying Newton’s iterative scheme. The computational approach has many advantages. One of the most important is to obtain the continuous and differentiable solution for FIDEs without using the operational matrix. Also, the convergence analysis is discussed in detail. At last, several numerical experiments are employed to clarify the performance and efficiency of the suggested method.

Keywords

  • Hahn wavelets,
  • Fractional-order integro-differential equations,
  • Laplace transform,
  • Collocation method,
  • Convergence analysis

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