Vasile Lupulescu

On a class of fuzzy functional differential equations

In this paper, we establish the local and global existence and uniqueness results for fuzzy functional differential equations. For the local existence and uniqueness we use the method of successive approximations and for global existence and uniqueness we use the contraction principle. Also, we apply these results to fuzzy differential equations with distributed delays and fuzzy population models.

Fuzzy fractional integral equations under compactness type condition

In this paper we study a fuzzy fractional integral equation. The fractional derivative is considered in the sense of Riemann-Liouville and we establish existence of the solutions of fuzzy fractional integral equations using the Hausdorff measure of noncompactness.

Fractional calculus for interval-valued functions

Abstract We use a generalization of the Hukuhara difference for closed intervals on the real line to develop a theory of the fractional calculus for interval-valued functions. The properties of Riemann–Liouville fractional integral, Riemann–Liouville fractional derivative and Caputo fractional derivative for interval-valued functions are investigated. Several examples are presented to illustrate the concepts and results.

Initial value problem for fuzzy differential equations under dissipative conditions

A new concept of inner product on the fuzzy space (E^n,D) is introduced, studied and used to prove several theorems stating the existence, uniqueness and boundedness of solutions of fuzzy differential equations. A stability result is also proved in the same context.

Hukuhara differentiability of interval-valued functions and interval differential equations on time scales

Abstract Using the concept of the generalized Hukuhara difference, in this paper we introduce and study the differentiability and the integrability for the interval-valued functions on time scales. Some illustrative examples to interval differential equations on time scales are presented.

A Schauder fixed point theorem in semilinear spaces and applications

In this paper we present existence and uniqueness results for a class of fuzzy fractional integral equations. To prove the existence result, we give a variant of the Schauder fixed point theorem in semilinear Banach spaces.MSC:34A07, 34A08.

On controllability and observability for a class of linear impulsive dynamic systems on time scales

The aim of this paper is to study the controllability and observability for a class of linear time-varying impulsive control systems on time scales. Sufficient and necessary conditions for state controllability and state observability of such systems are established. The corresponding criteria for time-invariant impulsive control systems on time scales are also obtained.

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.

Existence and uniqueness of solutions for random fuzzy fractional integral and differential equations

In this paper the random fuzzy fractional integral and differential equations are introduced. Under Lipschitz condition we obtain the existence and uniqueness theorems of solutions for two general forms of random fuzzy fractional integral equations. To prove this assertion we use an idea of successive approximations. Moreover, the approach is followed to prove the existence and uniqueness of solutions for random fuzzy fractional initial value problem under Caputo-type fuzzy fractional derivatives. The method is illustrated by solving an example.