The purpose of this study is to look at a family of starting value problem for semilinear fuzzy fractional elliptic equation with fractional Caputo derivatives. Firstly, we are going to extend the definition of laplacian operator under generalized H-differentiability in the Fuzzy systems. Secondly, the fuzzy integral equation are founded. Then, the existence and uniqueness of a fuzzy solution are etablished utilizing the Banach fixed point assessment method under Lipschitz conditions. Finally, we conclude our work by a conclusion.

In this paper, we investigate the existence and uniqueness solutions for a fuzzy Neutral fractional integro-differential equation with non-local conditions. First, we show the existence of solutions with the help of the Non-linear alternative for one-value function, as well as Krasnoselskii’s and Banach’s fixed point theorems. Moreover, we examine the generalized Ulam Hyers (GUH) and Ulam Hyers Rassias stability for our main problem. Finally, an example is presented to show the usability of our major results.

In this paper, we investigate the existence and uniqueness of solutions for fuzzy boundary value problems involving fuzzy Caputo fractional derivatives of order q 2 (2, 3). As a preliminary step, we construct a generic structure of the solution associated with our proposed model by utilizing the Green’s function. We establish the existence of a unique solution of the proposed model paired with the given initial conditions by using Banach fixed point theorem. At last, as application, an illustrative example is given to show the applicability of our theoritical results.

In this work, we discuss solutions to the abstract Cauchy problem of fuzzy conformal fractional. In addition, the method of fuzzy fractional semigroups is used to obtain analytical solutions to the fractional differential equation. We use the concept of Krasnoselskiis fixed point theorem to determine the existence and uniqueness of the solution. An application is also given to illustrate our main abstract results.

In this research, we provide certain novel requirements for the existence and uniqueness of fuzzy solutions for a type of nonlinear fuzzy Caputo fractional generalized Hukuhara Volterra–Fredholm integro-differential equations under integral boundaries. The required findings are demonstrated by employing the Banach and successive iterations convergence technique. First, we give the two analytic form solution equivalent the main equation and then we show the existence and uniqueness of solutions with the help of the successive iterations convergence technique, as well as Banach’s fixed point theorem. Moreover, we examine the generalized Ulam–Hyers (GUH) and Ulam–Hyers–Rassias stability for our main problem. An example is provided to demonstrate the reliability of our findings.