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Some results for fractional boundary value problem of differential inclusions. (English) Zbl 1169.34006
The author studies the existence of at least one solution of a (R-L sense) fractional-order (with order in (1,2)) differential inclusion with Dirichlet boundary conditions. The two cases, convex and nonconvex set-valued right-hand side are considered. The main tools of the proof are the nonlinear alternative Lary-Schauder type, Covitz-Nadler’s fixed point theorem for the set-valued contractions. The compactness of the set of solutions and relaxation results are also established. The infinite delay problem has been considered.
MSC:
34A60Differential inclusions
26A33Fractional derivatives and integrals (real functions)
26A42Integrals of Riemann, Stieltjes and Lebesgue type (one real variable)
47N20Applications of operator theory to differential and integral equations