Solving Fractional Differential Equations with Laplace Transform and Picard Iteration

Abstract

^{This paper explores approximate analytical solutions for a class of fractional differential equations involving the Caputo fractional derivative. The proposed method employs the Laplace transform in conjunction with the Picard iterative technique to derive solutions with improved accuracy and simplicity. The Caputo derivative's distinct formulation enables an intuitive representation of initial conditions, facilitating its application in various scientific and engineering problems. The study outlines the theoretical foundation of the approach, demonstrating its efficiency through illustrative examples. Results indicate that this methodology provides a reliable framework for addressing the complexities of fractional differential equations, offering insights into their behavior and practical applications.}