An operational matrix approach with Vieta-Fibonacci polynomial for solving generalized Caputo fractal-fractional differential equations

Abstract

This study developed and examined a new operational matrix approach utilizing the Vieta-Fibonacci polynomial for the numerical solution of generalized Caputo-type differential equations with fractal-fractional terms. Based on the proposed approach, the fractal-fractional differential equations with generalized Caputo-type derivatives were reduced into a system of algebraic equations, which was further solved to obtain the unknown solution. The convergence and error bounds are theoretically calculated. The results are quantitatively confirmed in various cases. To demonstrate the correctness and computational efficacy of this proposed technique, it is compared to other well-known methods.

Keywords

• Fractal-fractional derivatives
• Vieta-Fibonacci polynomials
• Operational matrix
• Convergence
• Error bound