Operational matrix approach for solving variable-order fractional integro-differential equations

In this paper, we use shifted fourth-kind Chebyshev polynomials to construct the operational matrix technique for numerical solution of variable-order fractional integro-differential equations (VO-FIDEs). We construct both fractional differential and integral operational matrices. These matrices coincide with the Chebyshev collocation method used to transform the main problem into an algebraic system of equations. By solving this system of equations we get the numerical solution of the original equation. Finally, we give several numerical examples to show that the numerical technique is applicable and computationally efficient. © 2023 Elsevier Inc. All rights reserved.