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

Abstract

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.

On the qualitative analyses solutions of new mathematical models of integro‐differential equations with infinite delay

“…Kumar et al [26] presented a convergent collocation method with which to find the numerical solution of a generalized fractional integro-differential equation. The presented approach of Kumar et al [26] is based on the collocation method using Jacobi poly-fractonomials.…”

“…Kumar et al [26] presented a convergent collocation method with which to find the numerical solution of a generalized fractional integro-differential equation. The presented approach of Kumar et al [26] is based on the collocation method using Jacobi poly-fractonomials. In Kumar et al [26], the generalized fractional integro-differential equation was defined in terms of the B-operator introduced recently, and it reduces to Caputo fractional derivative and other fractional derivatives in special cases.…”

“…The presented approach of Kumar et al [26] is based on the collocation method using Jacobi poly-fractonomials. In Kumar et al [26], the generalized fractional integro-differential equation was 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 were also established.…”

A nonlinear fractional partial integro‐differential equation with nonlocal initial value conditions

“…There are some recent studies on several general classes of fractional-order kinetic equations using various approaches [6,[10][11][12]. In addition, researchers have investigated the existence and uniqueness for various types of fractional integro-differential equations, with boundary conditions and the Hilfer derivative, via different methods [13][14][15][16].…”

Numerical solution of system of Fredholm-Volterra integro-differential equations using Legendre polynomials

“…Some dynamical models involving fractional-order derivatives with the Mittag-Leffler type kernels and their applications based upon the Legendre spectral collocation method have been investigated by Srivastava et al [36]. Kumar et al [37] presented a convergent collocation method based on Jacobi poly-fractonomials with which to find the numerical solution of a generalized fractional integro-differential equation. Izadi and Srivastava [38] investigated a novel set of orthogonal basis functions combined with a matrix technique for treating a class of multi-order fractional pantograph differential equations computationally.…”