Genocchi collocation method for accurate solution of nonlinear fractional differential equations with error analysis

Abstract

In this study, we introduce an innovative fractional Genocchi collocation method for solving nonlinear fractional differential equations, which have significant applications in science and engineering. The fractional derivative is defined in the Caputo sense and by leveraging fractional-order Genocchi polynomials, we transform the nonlinear problem into a system of nonlinear algebraic equations. A novel technique is employed to solve this system, enabling the determination of unknown coefficients and ultimately the solution. We derive the error bound for our proposed method and validate its efficacy through several test problems. Our results demonstrate superior accuracy compared to existing techniques in the literature, suggesting the potential for extending this approach to tackle more complex problems of critical physical significance.