On approximate solutions for a class of semilinear fractional-order differential equations in Banach spaces

We apply the topological degree theory for condensing maps to study approximation of solutions to a fractional-order semilinear differential equation in a Banach space. We assume that the linear part of the equation is a closed unbounded generator of a C0-semigroup. We also suppose that the nonlinearity satisfies a regularity condition expressed in terms of the Hausdorff measure of noncompactness. We justify the scheme of semidiscretization of the Cauchy problem for a differential equation of a given type and evaluate the topological index of the solution set. This makes it possible to obtain a result on the approximation of solutions to the problem. © 2017, The Author(s).

Authors
Kamenskii M.1 , Obukhovskii V. 2, 3 , Petrosyan G.2 , Yao J.-C.4
Publisher
Springer International Publishing
Number of issue
1
Language
English
Status
Published
Number
28
Volume
2017
Year
2017
Organizations
  • 1 Faculty of Mathematics, Voronezh State University, Voronezh, 394006, Russian Federation
  • 2 Faculty of Physics and Mathematics, Voronezh State Pedagogical University, Voronezh, 394043, Russian Federation
  • 3 RUDN University, 6 Miklukho-Maklaya st., Moscow, 117198, Russian Federation
  • 4 Center for General Education, China Medical University, Taichung, 40402, Taiwan
Keywords
approximation; Cauchy problem; condensing map; fixed point; fractional differential equation; index of the solution set; measure of noncompactness; semidiscretization; semilinear differential equation
Date of creation
19.10.2018
Date of change
19.10.2018
Short link
https://repository.rudn.ru/en/records/article/record/5143/
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