An effective operational-collocation method for approximating Bessel fractional derivative

Abstract

In this work, we establish the operational matrices for the Bessel fractional derivative (FDe) and the Riesz FDe applying the shifted Legendre polynomials. This technique is applied for the numerical study Euler–Poisson–Darboux equation involving distributed-order Bessel FDe and the spatial Riesz FDe. Additionally, three numerical illustrations are conducted to demonstrate the effectiveness and trustworthiness of the proposed techniques.