Fuzzy functional integro-differential equations under generalized H-differentiability

Abstract

In this paper, we present the studies on two kinds of solutions to fuzzy functional integro-differential equations (FFIDEs). The different types of solutions to FFIDEs are generated by the usage of two different concepts of fuzzy derivative in the formulation of a differential problem. Some examples are given to illustrate these results.

Ulam‐Hyers Stability and Ulam‐Hyers‐Rassias Stability for Fuzzy Integrodifferential Equation

“…( ) = [ ( ),̃( )] for any ∈ , then Hoa et al[4], we obtain ( ) = 0 for any ∈ . This completes the proof.…”

“…Fuzzy differential and integrodifferential equation (FD-FIDE) are a natural way to model dynamical systems subject to uncertainties. In the past few years, the study of fuzzy integrodifferential equations is an area of mathematics that has recently received a lot of attention (see, e.g., [1][2][3][4][5][6][7][8][9][10][11]). Alikhani et al [3] studied the existence and uniqueness of global solutions for fuzzy initial value problems via integrodifferential operators of Volterra type.…”

“…Using this concept, authors proved the existence and uniqueness of global solutions of an initial value problem for first-order nonlinear FIDE under generalized differentiability. Additionally, authors [4] studied the two kinds of solutions to FIDE with delay by the usage of two different concepts of fuzzy derivative.…”

Random fuzzy functional integro-differential equations under generalized Hukuhara differentiability

“…The strongly generalized differentiability was introduced in [7] and studied in [3,4,5,6,11,20,28,29,30,39].…”

On the Existence and Uniqueness for High Order Fuzzy Fractional Differential Equations with Uncertainty

“…., one of the important and interesting transforms in the problems of fuzzy equations is Laplace transforms. The fuzzy Laplace transform method solves fuzzy fractional differential equations and fuzzy boundary and initial value problems [35][36][37][38] . .…”