Coupled Fractional Volterra Integral Equations With Fuzzy Operators in ∗‐Fuzzy Measure Spaces: Stability Analysis and Hamacher ∗‐Fuzzy Numerical Approximation
Mahdis Yazdani Gharehaghaj, Reza Saadati, Mohammad Bagher Ghaemi
Source abstract
In this paper, we study a coupled system of fractional Volterra integral equations in the ∗‐fuzzy measure spaces that are equipped with an Archimedean triangular norm and a ∗‐fuzzy integral. Setting a Lipschitz condition on the nonlinear kernels, defining a suitable ∗‐fuzzy control function, and applying the alternative fixed‐point method, we obtain existence, uniqueness, and Hyers–Ulam stability of this system in an admissible ∗‐fuzzy function space. We also analyze the Lipschitz‐type dependence of the solution on the fractional orders over compact intervals. Finally, we consider the Hamacher ∗‐fuzzy product‐integration Picard scheme and solve the equation numerically. Our results extend and enhance the previous studies in the literature.
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