A numerical method based on quadrature rules for *-fractional differential equations

This paper presents a numerical method for the solution of a class of *-fractional differential equations involving Caputo derivative with respect to a function. Initial value problem for the certain *-fractional differential equation is converted into equivalent second kind of Volterra integral equation. A combination of Simpson's and Trapezoidal rule is used to transform the Volterra equation into a system of algebraic equations. The numerical solutions to the original problem are recovered from a solution of an algebraic system. We also give an error estimate for the function approximation and fractional integral approximation. Error bound for the numerical approximation of solutions is also derived. The numerical method is tested for various specific problems.(c) 2022 Elsevier B.V. All rights reserved.

Automated summary

This paper presents a numerical method for solving a class of *-fractional differential equations involving Caputo derivative with respect to a function. The method converts the initial value problem into an equivalent second kind of Volterra integral equation and utilizes a combination of Simpson's and Trapezoidal rule to transform it into a system of algebraic equations. The original problem's numerical solutions are recovered from a solution of the algebraic system. Error estimates for function approximation and fractional integral approximation are provided, along with an error bound for the numerical approximation of solutions. The method is tested for various specific problems.