A Novel Hybrid VIM-Abaoub Shkheam Scheme for Solving Linear and Nonlinear Fuzzy Fractional Differential Equations
DOI:
https://doi.org/10.65405/q0zfkb48الكلمات المفتاحية:
Fuzzy Fractional Differential Equations (FFDEs); Variational Iteration Method (VIM); Abaoub-Shkheam Transform; Caputo Fractional Derivativeالملخص
This paper introduces a novel hybrid computational framework, the VIM-Abaoub Shkheam Method, designed to solve linear and nonlinear Fuzzy Fractional Differential Equations (FFDEs) under Caputo derivative. The proposed approach integrates the Abaoub-Shkheam transform—a robust fractional integral transform—with the Variational Iteration Method (VIM) to eliminate the complexities associated with fuzzy fractional integration. For nonlinear systems, such as the Fuzzy Fractional Riccati Equation, the method is synergized with Adomian Polynomials to maintain high numerical fidelity without the need for linearization or discretization. Theoretical convergence is rigorously established using the Banach contraction mapping principle. Numerical results demonstrate that the method perfectly preserves the fuzzy containment property, with lower and upper bounds converging precisely to the crisp core at A comparative analysis reveals that while linear models exhibit stable uncertainty expansion, nonlinear models demonstrate an accelerated uncertainty growth ratio of up to 1.87, highlighting the method's sensitivity in capturing complex fuzzy dynamics. The results confirm that the VIM-Abaoub Shkheam method is an efficient, stable, and versatile tool for modeling uncertainty in fractional-order dynamic systems.
التنزيلات
المراجع
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