Numerical Technique for Solving Fractional Generalized Pantograph-Delay Differential Equations by Using Fractional-Order Hybrid Bessel Functions

Abstract

This paper introduces a new computational technique for dealing with fractional generalized pantograph-delay differential equations (PDDEs). The main idea of the proposed method is based on the fractional-order hybrid Bessel functions (FHBFs), which are constructed by the combination of fractional Bessel functions with block-pulse functions. The fractional derivative is applied in the Caputo sense. In the numerical technique, the operational matrix of fractional derivative is applied to reduce fractional generalized PDDEs to a system of algebraic equations with unknown fractional-order hybrid Bessel coefficients. In addition, the estimation of the error is analyzed. The error analysis indicates that when the number of FHBFs bases is increased, the obtained results convergent to the exact solution. Illustrative examples will be examined to demonstrate the validity and applicability of the presented technique. Also, the outcomes in comparison with the existing results in other methods illustrate the preference of the presented method.