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.
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.
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...
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.
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.
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.
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...
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.
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