A new approach of generalized shifted Vieta-Fibonacci polynomials to solve nonlinear variable order time fractional Burgers-Huxley equations

Abstract In recent years, advancements in optimization techniques and the widespread availability of high-performance computing have made it increasingly feasible to study and develop approximation strategies for nonlinear models. This progress has empowered researchers to address more intricate and realistic challenges associated with these models. This paper introduces the application of a novel polynomial, the generalized shifted Vieta-Fibonacci polynomials (GSVFPs), in solving nonlinear variable order time fractional Burgers-Huxley equations. To mitigate storage and computational costs, new operational matrices (OMs) are devised. The proposed algorithm integrates GSVFPs, OMs, and Lagrange multipliers to achieve optimal approximations. Through convergence analysis and numerical examples, the effectiveness and accuracy of the proposed algorithm in solving these equations are demonstrated. The provided numerical illustrations further bolster this assertion.