Initial and boundary value problem of fuzzy fractional-order nonlinear Volterra integro-differential equations

The fractional derivative in Caputo sense for the class of fuzzy fractional order Volterra integro-differential equations of the first kind is examined in this article. This paper considers both the initial and boundary value problems simultaneously. The transformation of first kind to second kind is done using Leibniz rule. Fixed point theory is used to establish the existence and uniqueness of the considered equation in its second kind. Furthermore, the Adomian decomposition method is used to determine the solution to the proposed problem. We provide some examples to back up the approach. The numerical and graphical representations of the symmetry between lower and upper cut representations of the fuzzy solutions are shown using MATLAB. A graphical representation is supported to critically examine how such methods work.