New approach for studying nonlocal problems related to differential systems and partial differential equations in generalized fuzzy metric spaces

Abstract

This study considers the solvability of nonlocal problems for fuzzy differential systems under gH-differentiability. Using some linear transforms, we convert partial differential equations into fuzzy integral systems, before some similar results are obtained for fuzzy wave equations with nonlocal conditions. As a consequence, we give some further estimates of the convergence rates of approximation schemes to exact solutions. The main tool used in our proofs is based on Perov's fixed point principle, which is applied to vector-valued integral operators. These operators appear as the sum of two integral operators, where one is Fredholm type and the other is of a Volterra type that depends on the restriction of the domain. The novel feature of this study is that we combine the matrix convergent to zero technique with calculations of fuzzy-valued functions in generalized fuzzy metric spaces. Some examples are presented to demonstrate our theoretical results.