10.57647/mathsci.2026.2002.12

A New Method for Nonlinear Katugampola Fractional Differential Equations

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  • Maham Bint E Ali1,
  • Shafaq Idrees1,
  • Umer Saeed*2,
  1. Department of Mathematics, School of Natural Sciences, National University of Sciences and Technology (NUST), Islamabad, Pakistan
  2. NUST Institute of Civil Engineering, School of Civil and Environmental Engineering, National University of Sciences and Technology (NUST), Islamabad, Pakistan

Received: 2025-10-03

Revised: 2026-01-21

Accepted: 2026-02-05

Published in Issue 2026-06-30

Copyright (c) 2026 Maham Bint-e-Ali, Shafaq Idrees, Umer Saeed (Author)

Creative Commons License

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

How to Cite

Bint E Ali, M., Idrees, S., & Saeed, U. (2026). A New Method for Nonlinear Katugampola Fractional Differential Equations. Mathematical Sciences, 20(2 (June 2026). https://doi.org/10.57647/mathsci.2026.2002.12
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Abstract

In this article, we propose a new wavelet method for solving nonlinear Katugampola fractional differential equations on an arbitrary interval. We have introduced a new wavelet, which we named as the Katugam-pola Gegenbauer wavelet (KGW), and constructed its new operational matrices of Katugampola fractional integrations as well as Katugampola fractional derivatives. The Katugampola Gegenbauer wavelet and its operational matrices are combined with the Adomian polynomials to propose a new method for the solution of nonlinear Katugampola fractional differential equations. The purpose of using the Adomian polynomials is to handle the nonlinearities in the equations. Furthermore, we have provided a detailed methodology for implementing the proposed approach to nonlinear Katugampola fractional differential equations. A detailed error analysis is also performed for the proposed method. The proposed method is implemented on several nonlinear Katugampola fractional differential equations to show the reliability, efficiency, and accuracy of the method.

Keywords

  • Katugampola fractional differential equations,
  • Katugampola Gegenbauer wavelet,
  • New operational matrices,
  • Adomian polynomials
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