Solving Distributed-Order Fractional Equations via Genocchi Wavelets and Weighted Residual Method
نویسندگان
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
doi
10.22052/mir.2025.256348.1503چکیده
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.
