On the existence of solutions for a differential inclusion of fractional order with upper-semicontinuous right-hand side

1999 ◽  
Vol 51 (11) ◽  
pp. 1764-1768
Author(s):  
A. N. Vityuk
Keyword(s):  
Differential Inclusion ◽  
Fractional Order ◽  
Existence Of Solutions ◽  
Upper Semicontinuous ◽  
Right Hand

scholarly journals ON FRACTIONAL DIFFERENTIAL INCLUSION PROBLEMS INVOLVING FRACTIONAL ORDER DERIVATIVE WITH RESPECT TO ANOTHER FUNCTION

Fractals ◽  
2020 ◽  
Vol 28 (08) ◽  
pp. 2040002 ◽  
Author(s):  
SAMIHA BELMOR ◽  
F. JARAD ◽  
T. ABDELJAWAD ◽  
MANAR A. ALQUDAH
Keyword(s):  
Differential Inclusion ◽  
Fractional Order ◽  
Nonlinear Boundary ◽  
Existence Of Solutions ◽  
Research Work ◽  
Main Tool ◽  
Nonlinear Boundary Value Problems ◽  
Inclusion Problems ◽  
Contractive Maps ◽  
Fractional Differential

In this research work, we investigate the existence of solutions for a class of nonlinear boundary value problems for fractional-order differential inclusion with respect to another function. Endpoint theorem for [Formula: see text]-weak contractive maps is the main tool in determining our results. An example is presented in aim to illustrate the results.

scholarly journals Bounded Motions of the Dynamical Systems Described by Differential Inclusions

2009 ◽  
Vol 2009 ◽  
pp. 1-9
Author(s):  
Nihal Ege ◽  
Khalik G. Guseinov
Keyword(s):  
Dynamical System ◽  
Dynamical Systems ◽  
Differential Inclusion ◽  
Differential Inclusions ◽  
Sufficient Conditions ◽  
Invariant Sets ◽  
Control Vector ◽  
Upper Semicontinuous ◽  
Right Hand ◽  
The Right

The boundedness of the motions of the dynamical system described by a differential inclusion with control vector is studied. It is assumed that the right-hand side of the differential inclusion is upper semicontinuous. Using positionally weakly invariant sets, sufficient conditions for boundedness of the motions of a dynamical system are given. These conditions have infinitesimal form and are expressed by the Hamiltonian of the dynamical system.

scholarly journals On a Multipoint Boundary Value Problem for a Fractional Order Differential Inclusion on an Infinite Interval

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Nemat Nyamoradi ◽  
Dumitru Baleanu ◽  
Ravi P. Agarwal
Keyword(s):  
Boundary Value Problem ◽  
Differential Inclusion ◽  
Fractional Order ◽  
Fixed Point Theorems ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Multipoint Boundary ◽  
Liouville Fractional Derivative ◽  
The Right ◽  
Multipoint Boundary Value Problem

We investigate the existence of solutions for the following multipoint boundary value problem of a fractional order differential inclusionD0+αut+Ft,ut,u′t∋0,0<t<+∞,u0=u′0=0,Dα-1u+∞-∑i=1m-2‍βiuξi=0, whereD0+αis the standard Riemann-Liouville fractional derivative,2<α<3,0<ξ1<ξ2<⋯<ξm-2<+∞, satisfies0<∑i=1m-2‍βiξiα-1<Γ(α),  and  F:[0,+∞)×ℝ×ℝ→𝒫(ℝ)is a set-valued map. Several results are obtained by using suitable fixed point theorems when the right hand side has convex or nonconvex values.

Existence of solutions for a second order boundary value problem with the Clarke subdifferential

Filomat ◽  
2017 ◽  
Vol 31 (9) ◽  
pp. 2763-2771 ◽  
Author(s):  
Dalila Azzam-Laouir ◽  
Samira Melit
Keyword(s):  
Boundary Value Problem ◽  
Differential Inclusion ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Second Order ◽  
Clarke Subdifferential ◽  
Lipschitzian Function ◽  
The Clarke Subdifferential

In this paper, we prove a theorem on the existence of solutions for a second order differential inclusion governed by the Clarke subdifferential of a Lipschitzian function and by a mixed semicontinuous perturbation.

scholarly journals Positive Solvability for Conjugate Fractional Differential Inclusion of (k,n-k) Type without Continuity and Compactness

Axioms ◽  
2021 ◽  
Vol 10 (3) ◽  
pp. 170
Author(s):  
Ahmed Salem ◽  
Aeshah Al-Dosari
Keyword(s):  
Differential Inclusion ◽  
Existence Of Solutions ◽  
Inclusion Type ◽  
Fractional Differential Inclusion ◽  
Fractional Differential

The monotonicity of multi-valued operators serves as a guideline to prove the existence of the results in this article. This theory focuses on the existence of solutions without continuity and compactness conditions. We study these results for the (k,n−k) conjugate fractional differential inclusion type with λ>0,1≤k≤n−1.

scholarly journals Fractional order differential inclusions on an unbounded domain with infinite delay

Mathematica ◽  
2020 ◽  
Vol 62 (85) (2) ◽  
pp. 167-178
Author(s):  
Mohamed Helal
Keyword(s):  
Fractional Order ◽  
Initial Value Problems ◽  
Differential Inclusions ◽  
Existence Of Solutions ◽  
Infinite Delay ◽  
Sufficient Conditions ◽  
Fréchet Spaces ◽  
Initial Value ◽  
Nonlinear Alternative ◽  
Hyperbolic Differential Inclusions

We provide sufficient conditions for the existence of solutions to initial value problems, for partial hyperbolic differential inclusions of fractional order involving Caputo fractional derivative with infinite delay by applying the nonlinear alternative of Frigon type for multivalued admissible contraction in Frechet spaces.

Semilinear fractional order integro-differential inclusions with infinite delay

2018 ◽  
Vol 25 (3) ◽  
pp. 317-327 ◽  
Author(s):  
Khalida Aissani ◽  
Mouffak Benchohra ◽  
Mohamed Abdalla Darwish
Keyword(s):  
Banach Spaces ◽  
Fractional Order ◽  
Differential Inclusions ◽  
Existence Of Solutions ◽  
Infinite Delay ◽  
Mild Solutions ◽  
Sufficient Conditions ◽  
Multivalued Maps ◽  
Nonlinear Alternative

AbstractIn this paper, we study the existence of mild solutions for a class of semilinear fractional order integro-differential inclusions with infinite delay in Banach spaces. Sufficient conditions for the existence of solutions are derived by using a nonlinear alternative of Leray–Schauder type for multivalued maps due to Martelli. An example is given to illustrate the theory.

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