A Convergent Collocation Approach for Generalized Fractional Integro-Differential Equations Using Jacobi Poly-Fractonomials

In this paper, we present a convergent collocation method with which to find the numerical solution of a generalized fractional integro-differential equation (GFIDE). The presented approach is based on the collocation method using Jacobi poly-fractonomials. The GFIDE is defined in terms of the B-operator introduced recently, and it reduces to Caputo fractional derivative and other fractional derivatives in special cases. The convergence and error analysis of the proposed method are also established. Linear and nonlinear cases of the considered GFIDEs are numerically solved and simulation results are presented to validate the theoretical results.

Automated summary

This paper presents a convergent collocation method for finding the numerical solution of a generalized fractional integro-differential equation (GFIDE) using Jacobi poly-fractonomials. The GFIDE is defined in terms of the recently introduced B-operator and converges to Caputo fractional derivative and other fractional derivatives in special cases. The method's convergence and error analysis are established, and simulation results validate the theoretical findings for both linear and nonlinear cases of the considered GFIDEs.