ファジィ分数階積分微分方程式の境界条件付き解の存在と一意性

Agilan K¹, Parthiban V², Nasreen Kausar³

¹Department of Mathematics, St. Joseph's College of Engineering, OMR, Chennai, 600119, Tamil nadu, India.

|January 6, 2026

Abstract:

The analytical behavior of fractional-order differential equations under uncertainty is often difficult to investigate. To address this challenge, this study considers Caputo-type fuzzy fractional Volterra integro-differential equations (FFVIDEs) with boundary conditions. An iterative numerical approach based on the Adomian decomposition method (ADM) is proposed to obtain approximate fuzzy solutions. The existence and uniqueness of the solution are established using Banach's fixed point theorem. Numerical simulations are carried out in MATLAB to illustrate the symmetry between the lower and upper ρ-cut representations of the fuzzy solutions. The graphical results demonstrate the accuracy and efficiency of the proposed method in handling uncertainty in fractional systems.

キーワード:

アドアム分解法分数階微分方程式不動点定理ファジィ分数階微分方程式

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