On fuzzy volterra-fredholm integrodifferential equation associated with hilfer-generalized proportional fractional derivative

Abstract

This investigation communicates with an initial value problem (IVP) of Hilfer-generalized proportional fractional (GPF) differential equations in the fuzzy framework is deliberated. By means of the Hilfer-GPF operator, we employ the methodology of successive approximation under the generalized Lipschitz condition. Based on the proposed derivative, the fractional Volterra-Fredholm integrodifferential equations (F VF IEs) via generalized fuzzy Hilfer-GPF Hukuhara differentiability (HD) having fuzzy initial conditions are investigated. Moreover, the existence of the solution is proposed by employing the fixed-point formulation. The uniqueness of the solution is verified. Furthermore, we derived the equivalent form of fuzzy F VF IEs which is supposed to demonstrate the convergence of this group of equations. Two appropriate examples are presented for illustrative purposes.