Solving Distributed-Order Fractional Equations via Genocchi Wavelets and Weighted Residual Method

Document Type : Original Scientific Paper

Authors

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

2 ‎Department of Mathematics Education, Farhangian University‎, ‎P.O‎. ‎Box 14665-889‎, ‎Tehran‎, ‎I‎. ‎R‎. ‎Iran

3 ‎Department of Mathematics Education, Faculty of Mathematics and Computer‎, ‎Shahid Bahonar University, Kerman‎, ‎I‎. ‎R‎. ‎Iran

Abstract

‎In this work‎, ‎a novel method to finding the numerical solution of distributed-order fractional differential equations (DFDEs) is introduced‎. ‎This method is based on the Genocchi wavelets (GWs)‎, ‎and weighted residual method (collocations method)‎. ‎For this aim‎, ‎an exact mathematical formula that incorporates regularized beta functions is meticulously formulated to ascertain the Riemann-Liouville fractional integral operator (R-LFIO) corresponding to these specific wavelets‎. ‎By employing the aforementioned integral operator and leveraging the capabilities of Gauss-Legendre numerical integration‎, ‎the original problem is adeptly transformed into a comprehensive system of algebraic equations‎, ‎thereby facilitating a more manageable analysis and solution process‎. ‎Also‎, ‎the error analysis is investigated and examples are given to demonstrate the effectiveness and accuracy of the method‎.

Keywords

Main Subjects

References

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Mathematics Interdisciplinary Research
Volume 11, Issue 1
March 2026
Pages 93-111

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