Applications of Elzaki Adomian Decomposition Method to Linear and Nonlinear Fractional-Order Differential Equations

الملخص

This paper explores the application of the Adomian Decomposition Method (ADM) to solve fractional-order differential equations (FDEs). The ADM is applied to both linear and nonlinear FDEs, with a focus on demonstrating its efficiency and accuracy in solving complex systems that involve fractional derivatives. The method is shown to decompose nonlinear equations into solvable series, providing an effective approach for obtaining analytical solutions without requiring simplifying assumptions. Numerical examples are presented to compare ADM with traditional methods, such as numerical integration and perturbation techniques, showcasing its advantages in terms of convergence and solution precision. The results confirm the method’s potential to solve practical and theoretical problems in fractional calculus, contributing to the advancement of this field.