Numerical Solutions of Fractional Weakly Singular Two-Dimensional Partial Volterra Integral Equations Using Euler Wavelets

Seyed Sadegh Gholami, Ali Ebadian, Amirahmad Khajehnasiri and Kareem T. Elgindy ()
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Seyed Sadegh Gholami: Department of Mathematics Education, Farhangian University, Tehran 14665-889, Iran
Ali Ebadian: Department of Mathematics, Faculty of Science, Urmia University, Urmia 57179-44514, Iran
Amirahmad Khajehnasiri: Department of Mathematics, Faculty of Science, Urmia University, Urmia 57179-44514, Iran
Kareem T. Elgindy: Department of Mathematics and Sciences, College of Humanities and Sciences, Ajman University, Ajman P.O. Box 346, United Arab Emirates

Mathematics, 2025, vol. 13, issue 17, 1-16

Abstract: This paper presents an innovative numerical method for solving two-dimensional weakly singular Volterra integral equations, including fractional Volterra integral equations with weak singularities. Solving these equations in higher dimensions and in the presence of fractional and weak singularities is highly challenging. The proposed approach uses Euler wavelets (EWs) within an operational matrix (OM) framework combined with advanced numerical techniques, initially transforming these equations into a linear algebraic system and then solving it efficiently. This method offers very high accuracy, strong computational efficiency, and simplicity of implementation, making it suitable for a wide range of such complex problems, especially those requiring high speed and precision in the presence of intricate features.

Keywords: fractional integral equation; two-dimensional Euler wavelets; fractional derivative; operational matrix (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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