scholarly journals On antiperiodic boundary value problem for semilinear fractional differential inclusion with deviating argument in Banach space

2020 ◽  
Vol 12 (3) ◽  
pp. 69-80
Author(s):  
Garik Petrosyan
Keyword(s):  
Banach Space ◽  
Boundary Value Problem ◽  
Differential Inclusion ◽  
Boundary Value ◽  
Deviating Argument ◽  
Fractional Differential Inclusion ◽  
Fractional Differential

On a fractional differential inclusion with “maxima”

2016 ◽  
Vol 19 (5) ◽  
Author(s):  
Aurelian Cernea
Keyword(s):  
Fixed Point ◽  
Boundary Value Problem ◽  
Differential Inclusion ◽  
Fixed Point Theorems ◽  
Boundary Value ◽  
Existence Results ◽  
Fractional Differential Inclusion ◽  
Right Hand ◽  
Fractional Differential ◽  
The Right

Abstract We study a boundary value problem associated to a fractional differential inclusion with “maxima”. Several existence results are obtained by using suitable fixed point theorems when the right hand side has convex or non convex values.

On a fractional differential inclusion with integral boundary conditions in Banach space

2013 ◽  
Vol 16 (3) ◽  
Author(s):  
Phan Phung ◽  
Le Truong
Keyword(s):  
Banach Space ◽  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Fractional Derivative ◽  
Differential Inclusion ◽  
Integral Boundary Conditions ◽  
Young Measures ◽  
Integral Boundary ◽  
Liouville Fractional Derivative ◽  
Fractional Differential

AbstractWe consider a class of boundary value problem in a separable Banach space E, involving a nonlinear differential inclusion of fractional order with integral boundary conditions, of the form (*)$\left\{ \begin{gathered} D^\alpha u(t) \in F(t,u(t),D^{\alpha - 1} u(t)),a.e.,t \in [0,1], \hfill \\ I^\beta u(t)|_{t = 0} = 0,u(1) = \int\limits_0^1 {u(t)dt,} \hfill \\ \end{gathered} \right. $ where D α is the standard Riemann-Liouville fractional derivative, F is a closed valued mapping. Under suitable conditions we prove that the solutions set of (*) is nonempty and is a retract in W Eα,1(I). An application in control theory is also provided by using the Young measures.

Sign in / Sign up

Export Citation Format

Share Document