Ngo Van Hoa

Fuzzy functional integro-differential equations under generalized H-differentiability

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.

Some global existence results and stability theorem for fuzzy functional differential equations

In this paper, we establish the global existence and uniqueness results for fuzzy functional differential equations (FFDEs) by using two different methods. We have extended and generalized some comparison theorems and stability theorem for FFDEs with definition a new Lyapunov-like function. Some examples are given to illustrate these results.

On Maximal and Minimal Solutions for Set-Valued Differential Equations with Feedback Control

In this paper, we present the existence of extremal solutions of set-valued differential equations with feedback control on semilinear Hausdorff space under Hukuhara derivative which is developed under the form , , for all with the monotone iterative technique and we will verify that monotone sequence of approximate solutions converging uniformly to the solution of the problem, that is useful for optimization problems.

The local existence of solutions for random fuzzy integro-differential equations under generalized H-differentiability

In this paper, we consider the random fuzzy integro-differential equations (RFIDEs) under generalized H- differentiability. The local existence of solutions for RFIDEs with initial conditions under generalized H-differentiability is studied. Two theorems for local existence of solutions are given and proved. Some examples are given to illustrate these results.

Existence of extremal solutions for interval-valued functional integro-differential equations

This paper is devoted to studying the maximal and minimal solutions for the interval-valued functional integro- differential equations (IFIDEs) under generalized Hukuhara differentiability by the method of upper and lower solutions and monotone iterative technique. Some examples are given to illustrate the results.

The initial value problem for interval-valued second-order differential equations under generalized H-differentiability

In this paper the interval-valued second-order differential equations under generalized Hukuhara differentiability (ISDEs) are introduced. Under suitable conditions we obtain the existence and uniqueness results of solutions to ISDEs. To prove this assertion we use idea of contraction principle and successive approximations. Furthermore, we use the method based on properties of linear transformations (LTM) to find the explicit solution of initial value problem for linear second-order differential equation with interval-valued forcing function and with interval initial values (IIVP). We apply the linear transformations method to two example problems including a vibrating mass and an electrical circuit. Finally, the method based on the analysis of a solution to real-valued second-order differential equation is investigated to solve interval-valued second-order differential equations with interval-valued coefficients, interval-valued forcing function and interval initial values. Some examples are presented to illustrate applicability of the proposed method.

Random fuzzy functional integro-differential equations under generalized Hukuhara differentiability

In this paper, we prove the existence and uniqueness results for the random fuzzy functional integro-differential equations under generalized Hukuhara differentiability. For the existence and uniqueness, we use the method of successive approximations. Some kinds of boundedness of the solution are established. Moreover, we provide examples to illustrate the results.

Interval-valued functional integro-differential equations

This paper is devoted to studying the local and global existence and uniqueness results for interval-valued functional integro-differential equations (IFIDEs). In the paper, for the local existence and uniqueness, the method of successive approximations is used and for the global existence and uniqueness, the contraction principle is a good tool in investigating. Some examples are given to illustrate the results.MSC:34G20, 34A12, 34K30.

Solving interval-valued fractional initial value problems under Caputo gH-fractional differentiability

Abstract In this paper interval-valued fractional differential equations (IFDEs) under Caputo generalized Hukuhara differentiability are introduced. We present existence and uniqueness results for IFDEs with a Krasnoselskii–Krein-type condition. The solution to interval-valued fractional initial value problems under Caputo-type interval-valued fractional derivatives by a modified fractional Euler method (MFEM) and a modified Adams–Bashforth–Moulton method (MABMM) is also presented.

Interval Abel integral equation

In this paper, we use a generalization of the Riemann–Liouville fractional integral for interval-valued functions to study a theory of the interval Abel integral equation (IAIE). Our aim is to clarify under which suitable conditions the IAIE is solvable. The theory is illustrated by solving some examples.