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On perturbed fractional differential inclusions with nonlocal multi-point Erdélyi-Kober fractional integral boundary conditions. (English) Zbl 1371.34005

In this paper by using a nonlinear alternative of a sum of compact upper semicontinuous and contractive multivalued operators, the authors establish sufficient conditions for the existence of solutions for the perturbed fractional differential inclusions \[ D^q x(t)\in F(t,x(t))+G(t,x(t)),\;t\in (0,T), \] where \(D^q\) is the standard Riemann-Liouville fractional derivative of order \(q\in (1,2],\) with nonlocal multi-point Erdélyi-Kober fractional integral boundary conditions \[ x(0)=0,\;\alpha x(T)=\sum_{i=1}^m \beta _i I_{\eta_i}^{\gamma_i,\delta_i}x ( \xi _i). \] For the applicability of the main result, the example is considered.

MSC:

34A08 Fractional ordinary differential equations
34A60 Ordinary differential inclusions
34B15 Nonlinear boundary value problems for ordinary differential equations
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