10.57647/ijm2c.2026.1603.18

A Study on Solving Fractional Volterra Integral Equations with Müntz Orthogonal Functions

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  • Fereshteh Roustaei1,
  • Majid Tavassoli Kajani1,
  • Maryam Bahmanpour*1,
  1. Department of Mathematics, Isf. C., Islamic Azad University, Isfahan, Iran

Received: 20-10-2025

Revised: 25-12-2025

Accepted: 27-12-2025

Published Online: 27-12-2025

Copyright (c) 2025 Fereshteh Roustaei, Majid Tavassoli Kajani, Maryam Bahmanpour (Author)

Creative Commons License

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

How to Cite

Roustaei, F., Tavassoli Kajani, M., & Bahmanpour, M. (2025). A Study on Solving Fractional Volterra Integral Equations with Müntz Orthogonal Functions. International Journal of Mathematical Modelling & Computations. https://doi.org/10.57647/ijm2c.2026.1603.18
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Abstract

In this paper, Müntz orthogonal functions are employed for the numerical solution of fractional Volterra integral equations. These functions are defined on the interval [0, 1] and possess simple and distinct real roots, providing the best unique approximation for functions in L2(0, 1). The Riemann–Liouville fractional integral operator is defined for these functions to reduce computational complexity and increase the solution speed. The error bound of the method is also determined. The numerical examples presented demonstrate the superiority of the proposed method compared to other existing approaches for the numerical solution of fractional Volterra integral equations. 

Keywords

  • Fractional Volterra integral Equations,
  • Orthogonal basis,
  • Müntz orthogonal functions,
  • Collocation method,
  • Function approximation,
  • Riemann–Liouville fractional integral operator
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