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

Abstract

We 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 formwhere 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 α,1 E (I). An application in control theory is also provided by using the Young measures.

On a Time-Fractional Integrodifferential Equation via Three-Point Boundary Value Conditions

“…Further results on positive solutions of a boundary value problem for nonlinear fractional differential equations were reported in [14] and new results on the existence results on nonlinear fractional differential equations were reported in [15]. For other related results we suggest for the readers [16,17] as well as the references therein. We recall that the existence of solutions for some fractional partial differential equations was investigated in [18,19] and the references therein.…”

Multiplicity Results for Integral Boundary Value Problems of Fractional Order with Parametric Dependence

“…In many of them the main results follow by means of suitable fixed point theorems [2,5,6,10,11,12,18,20]. In [6], Benchohra and Ouaar investigated the existence of solution of the nonlinear fractional differential equation with integral boundary condition:…”

On the existence of solutions for fractional differential inclusions with sum and integral boundary conditions

“…For instence, one can find a lot of papers in this field (see [1][2][3][4][5][10][11][12][13][14][15]17], and the references therein). Also, some researchers have been investigated the existence of solutions for some fractional differential inclusions (see for example, [2,3,[6][7][8]16,25,28,30]). …”