A novel analytical method for the multi-delay fractional differential equations through the matrix of clique polynomials of the cocktail party graph

Abstract

This paper provides a unique graph matrix approach based on the Clique polynomials of the Cocktail party graph to effectively solve multi-delay fractional differential equations (MDFDE) with variable coefficients. Clique polynomials of the cocktail party graph’s basis are used as a trial function for the solution of MDFDE. An operational matrix of Caputo fractional derivative of polynomial approximation is employed to transform the MDFDEs into a system of algebraic equations. The unknowns in the system are determined by Newton’s method in Mathematica. The productivity of the suggested strategy is examined with five numerical examples. From all the discussed examples, it is observed that the proposed Clique polynomial collocation method (CPCM) has excellent compatibility with linear MDFDEs by attaining an exact solution. To substantiate the validity of the recommended method, obtained results with comparisons, computation time, convergence analysis, error estimations, and graphical illustrations are offered.

Keywords

• Multi-delay fractional differential equations with variable coefficients
• Clique polynomial of cocktail party graph
• Collocation points
• Matrix method
• Convergence analysis