The minimax approach for a class of variable order fractional differential equation

Abstract

This paper introduces an approximate solution for Liouville‐Caputo variable order fractional differential equations with order 0 < α(t) ≤ 1. The solution is adapted using a family of fractional‐order Chebyshev functions with unknown coefficients. These coefficients have been obtained by using an optimization approach based on minimax technique and the least pth optimization function. Several linear and nonlinear fractional‐order differential equations are discussed using the proposed technique for fixed and variable order fractional‐order derivatives. Moreover, the response of RC charging circuit with variable order fractional capacitor is studied for different cases. Several comparisons with related published techniques have been added to illustrate the accuracy of the proposed approach.

An investigation of a closed-form solution for non-linear variable-order fractional evolution equations via the fractional Caputo derivative

“…They discussed the system of VO FDEs and estimated its parameters for one or more variables. Semary et al [7] approximated the solution of Liouville-Caputo VO FPDEs with 0 < α(t) ≤ 1 based on the Chebyshev function and discussed many linear and non-linear non-integer-order PDEs. Taghipour and Aminikhah [8] proposed the ADI numerical scheme for the fractional-order model and discussed the theoretical analysis.…”