Operational matrix for solving fractional differential equations with Erdelyi-Kober differential operator

• Published in: AIP Conference Proceedings
• Main Author: Nasrudin F.S.M.; Phang C.; Mahadi S.; Arbin N.
• Format: Conference paper
• Language: English
• Published: American Institute of Physics Inc. 2024
• Online Access: https://www.scopus.com/inward/record.uri?eid=2-s2.0-85182556246&doi=10.1063%2f5.0171631&partnerID=40&md5=5a56ac8c7a80c3efc85b746cf628b093

The operational matrix based on shifted Legendre polynomials is used in this study to solve Erdelyi-Kober (E-K) fractional differential equations. To do this, we derive the analytical expression for polynomial for E-K derivative of polynomial xk where k is positive integer. As a result, the operational matrix approach for the E-K derivative is developed by employing the characteristics of shifted Legendre polynomials for the first time here. The E-K fractional differential equations are then converted into a system of algebraic equations. We can acquire the numerical solution to fractional differential equations defined in the E-K derivative by solving that system. We simply need a small number of terms of shifted Legendre polynomials to get the accurate solution. © 2024 Author(s).