New properties of the first‐order Riemann–Liouville fractional integrals are proved and derivatives for equivalence class functions in analyzed. Solutions, normal solutions, generalized solutions initial value problems (IVPs) nonlinear differential equations (FDEs) with fraction introduced. The equivalences between FDEs corresponding (Volterra) integral established based on solutions. results e...

in this paper we intend to offer new numerical methods to solve the second-order fuzzy abel-volterraintegro-differential equations under the generalized $h$-differentiability. the existence and uniqueness of thesolution and convergence of the proposed methods are proved in details and the efficiency of the methods is illustrated through a numerical example.

In the present paper using homotopy analysis method (HAM), we approximate a special case of fuzzy integral equations. The fuzzy integral and integro-differential equations have a wide range of applications in science and engineering. In this paper HAM can be to find the exact solution or an approximate solution of the problem. Within this paper the HAM is used to obtain A series solution of int...

The focus of this paper is to clarify the concepts of solutions of linear equations in interval, probabilistic, and fuzzy sets setting for real world tasks. There is a fundamental difference between formal definitions of the solutions and physically meaningful concepts of solution in applied tasks, when equations have uncertain components. For instance, a formal definition of the solution in te...

It is shown that the attractor of an autonomous Caputo fractional differential equation order $$\alpha \in (0,1)$$ in $${\mathbb {R}}^d$$ whose vector field has a certain triangular structure and satisfies smooth condition dissipativity essentially same as ordinary with field. As application, we establish several one-parameter bifurcations for scalar equations including saddle-node pichfork bif...

This paper aims to contribute to research on the question of the stabilization or destabilization of a deterministic dynamical system (differential equation, partial differential equation, or functional differential equation) by a noise perturbation, and in particular, perturbations which transform the differential equation (or FDE) to one of Itô-type. Mao has written an interesting paper [9] d...

In this paper we use the fuzzy Caputo derivatives under generalized Hukuhara difference to introduce fuzzy fractional Volterra-Fredholm integro-differential equations and prove the existence and uniqueness of the solutions for this class of fractional equations.

In this paper,  The Picard method is proposed to solve the system of first-order fuzzy  differential equations  $(FDEs)$ with fuzzy initial conditions under generalized $H$-differentiability. Theexistence and uniqueness of the solution and convergence of theproposed method are proved in details. Finally, the method is illustrated by solving some examples.

In this paper, we consider fuzzy fractional partial differential equations under Caputo generalized Hukuhara differentiability. Some new results on the existence and uniqueness of two types of fuzzy solutions are studied via  weakly contractive mapping in the partially ordered metric space. Some application examples are presented to illustrate our main results.