A collocation approach for multiterm variable-order fractional delay-differential equations using shifted Chebyshev polynomials

Abstract

In this article, a general form of multiterm variable-order fractional delay differential equations (GVOFDDEs) is presented. The introduced GVOFDDEs have variable-order multi-terms and integer-order derivatives as well for all terms delayed or with normal argument. The variable order derivative is a generalization of fractional and integer orders, so it considered in this work. The collocation approach is applied with the aid of shifted Chebyshev polynomials to solve the presented GVOFDDEs as a matrix discretization technique. The presented technique transforms all terms of GVOFDDEs to a matrix equation with novel operational matrices. The qualification of the presented scheme is measured by many numerical test examples.

Keywords

• Variable-Order fractional delay-differential equations
• Shifted Chebyshev collocation method
• Caputo variable-Order fractional derivatives