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<p>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 <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\rho\)</EquationSource> </InlineEquation>-cut representations of the fuzzy solutions. The graphical results demonstrate the accuracy and efficiency of the proposed method in handling uncertainty in fractional systems.</p>

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Existence and uniqueness of solutions for fuzzy fractional integro-differential equations with boundary conditions

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年1月5日

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  • Agilan K.,
  • Parthiban V.,
  • Nasreen Kausar,
  • Mohammed Abdullah Salman

摘要

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 \(\rho\) -cut representations of the fuzzy solutions. The graphical results demonstrate the accuracy and efficiency of the proposed method in handling uncertainty in fractional systems.