A Novel Shifted Jacobi Operational Matrix Method for Linear Multi-terms Delay Differential Equations of Fractional Variable-order with Periodic and Anti-periodic Conditions

Abstract

This paper investigates the generalized linear multi-terms delay fractional differential equation of variable order with periodic and anti-periodic conditions. In this work, a novel shifted Jacobi operational matrix technique is applied to solve a class of these equations, so that the original problem becomes a system of algebraic equations that can be solved by numerical methods. The proposed technique is successfully applied to the aforementioned problem. Sufficient and complete numerical tests are presented to demonstrate the accuracy, generality, efficiency of presented technique and the flexibility of this scheme. The numerical results of this method are compared with other existing methods such as fractional backward differential formulas (FBDF). Comparing the outcomes of these schemes, as well as comparing the current technique (NSJOM) with the exact solution, demonstrates the efficiency and validity of this method. It should be noted that the implementation of current method is considered very easy and general for many numerical techniques. Furthermore, the error and its bound are estimated.