Papers by Vasile Lupulescu
arXiv: General Mathematics, 2019
In this paper we propose a new concept of differentiability for interval-valued functions. This c... more In this paper we propose a new concept of differentiability for interval-valued functions. This concept is based on the properties of the Hausdorff-Pompeiu metric and avoids using the generalized Hukuhara difference.
Professor Constatin Buşe, age 60, passed away on 4 February 2020 after a severe illness. Constant... more Professor Constatin Buşe, age 60, passed away on 4 February 2020 after a severe illness. Constantin Buşe was born on 19 October 1960 in Oteşani, County Vâlcea, Romania, where he attended the gymnasium studies. He continued his secondary education at the Energy High School of Râmnicu Vâlcea and in the years 1980-1984 he studied mathematics at the West University of Timişoara. Because in the 80's of the last century the teaching positions in Romanian university education were blocked and all graduates of mathematics faculties could choose only for a position in gymnasium school, high school or industry, Professor Constantin Buşe began his teaching career in 1984 as a teacher of mathematics at the Gymnasium School No.
Journal of Applied Nonlinear Dynamics, 2017
Journal of Intelligent & Fuzzy Systems, 2018
This paper highlights the mathematical model of biological experiments, that have an effect on ou... more This paper highlights the mathematical model of biological experiments, that have an effect on our lives. We suggest a mathematical model involving fractional differential operator, kind of hybrid iterative fractional differential equations. Our technique is based on monotonous iterative in the nonlinear analysis. The monotonous sequences described extremal solutions converging for hybrid monotonous fractional iterative differential equations. We apply the monotonous iterative method under appropriate conditions to prove the existence of extreme solutions. The tool relies on the Dhage fixed point Theorem. This theorem is required in biological studies in which increasing or decreasing know freshly split bacterial and could control.
Fuzzy Sets and Systems, 2018
Abstract In this note, we present some remarks on solutions of fractional fuzzy differential equa... more Abstract In this note, we present some remarks on solutions of fractional fuzzy differential equation. In general, a fractional fuzzy differential equation and a fractional fuzzy integral equation are not equivalent. In this paper we give an appropriate condition so that this equivalence is valid. Some examples are provided to illustrate the theory.
Journal of Integral Equations and Applications, 2017
This paper considers the existence of L psolutions for a class of fractional integral equations i... more This paper considers the existence of L psolutions for a class of fractional integral equations involving abstract Volterra operators in a separable Banach space. Some applications for the existence of L p-solutions for different classes of fractional differential equations are given. 2010 AMS Mathematics subject classification. Primary 34A07, 34A08.
Electronic Journal of Differential Equations, 2011
In this paper we study the existence and uniqueness of the solution for a class of fractional dif... more In this paper we study the existence and uniqueness of the solution for a class of fractional differential equation with fuzzy initial value. The fractional derivatives are considered in the Riemann-Liouville sense.
Computational and Applied Mathematics
Annals of the University of Craiova - Mathematics and Computer Science Series, 2003
In this paper we prove a existence result for a second order differential inclusion x′′ ∈ F (x, x... more In this paper we prove a existence result for a second order differential inclusion x′′ ∈ F (x, x′) , x (0) = x0, x′ (0) = y0, where F is an upper semicontinuous, compact valued multifunction, such that F (x, y) ⊂ ∂V (y), for some convex proper lower semicontinuous function V . 2000 Mathematics Subject Classification. Primary 34A60; Secondary 49J52.
Abstract. We prove the existence of solutions for the functional differential inclusion x ′ ∈ F (... more Abstract. We prove the existence of solutions for the functional differential inclusion x ′ ∈ F (T (t)x), where F is upper semi-continuous, compact-valued multifunction such that F (T (t)x) ⊂ ∂V (x(t)) on [0, T], V is a proper convex and lower semicontinuous function, and (T (t)x)(s) = x(t+ s). 1.
Proceedings of the Royal Society of Edinburgh: Section A Mathematics
Let q be a positive integer and let (an) and (bn) be two given ℂ-valued and q-periodic sequences.... more Let q be a positive integer and let (an) and (bn) be two given ℂ-valued and q-periodic sequences. First we prove that the linear recurrence in ℂ 0.1$$x_{n + 2} = a_nx_{n + 1} + b_nx_n,\quad n\in {\open Z}_+ $$is Hyers–Ulam stable if and only if the spectrum of the monodromy matrix Tq: = Aq−1 · · · A0 (i.e. the set of all its eigenvalues) does not intersect the unit circle Γ = {z ∈ ℂ: |z| = 1}, i.e. Tq is hyperbolic. Here (and in as follows) we let 0.2$$A_n = \left( {\matrix{ 0 & 1 \cr {b_n} & {a_n} \cr } } \right)\quad n\in {\open Z}_+ .$$Secondly we prove that the linear differential equation 0.3$${x}^{\prime \prime}(t) = a(t){x}^{\prime}(t) + b(t)x(t),\quad t\in {\open R},$$ (where a(t) and b(t) are ℂ-valued continuous and 1-periodic functions defined on ℝ) is Hyers–Ulam stable if and only if P(1) is hyperbolic; here P(t) denotes the solution of the first-order matrix 2-dimensional differential system 0.4$${X}^{\prime}(t) = A(t)X(t),\quad t\in {\open R},\quad X(0) = I_2,$$where I2...
Fuzzy Sets and Systems, 2016
We prove the existence of solutions for the functional differential inclusion x ∈ F (T (t)x), whe... more We prove the existence of solutions for the functional differential inclusion x ∈ F (T (t)x), where F is upper semi-continuous, compact-valued multifunction such that F (T (t)x) ⊂ ∂V (x(t)) on [0, T ], V is a proper convex and lower semicontinuous function, and (T (t)x)(s) = x(t + s).
Fuzzy Sets and Systems, 2007
In this paper, we establish the local and global existence and uniqueness results for fuzzy funct... more 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.
ABSTRACT We prove an existence result for the second-order differential inclusion x '&... more ABSTRACT We prove an existence result for the second-order differential inclusion x '' ∈F(x,x ' ),x(0)=x 0 ,x ' (0)=y 0 , where F is an upper semicontinuous, compact-valued multifunction, such that F(x,y)⊂∂V(y), for some convex proper lower semicontinuous function V.
Information Sciences an International Journal, Dec 1, 2008
A new concept of inner product on the fuzzy space (En,D) is introduced, studied and used to prove... more A new concept of inner product on the fuzzy space (En,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.
We prove a viability result for the second-order differential inclusion x ∈ F (x, x), (x(0), x (0... more We prove a viability result for the second-order differential inclusion x ∈ F (x, x), (x(0), x (0)) = (x0, y0) ∈ Q := K × Ω, where K is a closed and Ω is an open subsets of R m , and is an upper semicontinuous set-valued map with compact values, such that F (x, y) ⊂ ∂V (y), for some convex proper lower semicontinuous function V .
Electronic Journal of Qualitative Theory of Differential Equations, Jan 4, 2013
This paper deals with the resolvent, asymptotic stability and boundedness of the solution of time... more This paper deals with the resolvent, asymptotic stability and boundedness of the solution of time-varying Volterra integro-dynamic system on time scales in which the coefficient matrix is not necessarily stable. We generalize to a time scale some known properties about asymptotic behavior and boundedness from the continuous case. Some new results for the discrete case are obtained.
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Papers by Vasile Lupulescu