An Operational Matrix Technique Based on Chebyshev Polynomials for Solving Mixed Volterra-Fredholm Delay Integro-Differential Equations of Variable-Order

In this work, an algorithm for finding numerical solutions of linear fractional delay-integro-differential equations (LFDIDEs) variable-order (VO) is introduced. The operational matrices are used as discretization technique based on shifted Chebyshev polynomials (SCPs) the first kind with spectral collocation method. proposed VO-LFDIDEs have multiterms integer, fractional-order derivatives delayed or nondelayed and mixed Volterra-Fredholm integral terms. introduced model a more general form VO pantograph, neutral, Fredholm–Volterra integro-differential delay arguments. Caputo’s derivative operator to generate derivative. Operational presented all reliability efficiency scheme demonstrated by some experiments. Also, examples included improve validity applicability techniques. Finally, comparisons between method other methods were solve equation.