Existence and approximation of solutions to nonlocal boundary value problems for fractional differential inclusions

被引：12
作者：
Kamenskii M. [1 ]
Obukhovskii V. [2 ]
Petrosyan G. [2 ]
Yao J.-C. [3 ]
机构：
[1] Faculty of Mathematics, Voronezh State University, Voronezh
[2] Faculty of Physics and Mathematics, Voronezh State Pedagogical University, Voronezh
[3] Research Center for Interneural Computing, China Medical University Hospital, China Medical University, Kaohsiung
来源：
Fixed Point Theory and Applications | / 2019卷 / 1期
基金：
俄罗斯基础研究基金会;
关键词：
Approximation; Cauchy problem; Condensing map; Fixed point; Fractional differential equation; Index of the solution set; Measure of noncompactness; Semidiscretization; Semilinear differential equation;
D O I：
10.1186/s13663-018-0652-1
中图分类号：
学科分类号：
摘要：
We study a semilinear fractional order differential inclusion in a separable Banach space E of the form DqCx(t)∈Ax(t)+F(t,x(t)),t∈[0,T], where DqC is the Caputo fractional derivative of order 0 < q< 1 , A: D(A) ⊂ E→ E is a generator of a C-semigroup, and F: [ 0 , T] × E⊸ E is a nonlinear multivalued map. By using the method of the generalized translation multivalued operator and a fixed point theorem for condensing multivalued maps, we prove the existence of a mild solution to this inclusion satisfying the nonlocal boundary value condition: x(0) ∈ Δ (x) , where Δ : C([ 0 , T] ; E) ⊸ E is a given multivalued map. The semidiscretization scheme is developed and applied to the approximation of solutions to the considered nonlocal boundary value problem. © 2019, The Author(s).
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