A new class of operational matrices method for solving fractional neutral pantograph differential equations

Abstract

Abstract This paper uses new fractional integration operational matrices to solve a class of fractional neutral pantograph delay differential equations. A fractional-order function space is constructed where the exact solution lies in, and a set of orthogonal bases are given. Using them, we reduce the fractional delay differential equation to algebraic equations and get the approximate solution. Finally, we give the Legendre operational matrix of fractional integration to solve the equation as an example and show the efficiency of the method.

Keywords

• Operational matrix
• Neutral pantograph differential equations
• Riemann–Liouville fractional integration
• Caputo fractional differential