scholarly journals Stability Analysis of a Fractional Order Discrete Anti-Periodic Boundary Value Problem

2021 ◽  
Vol 12 (1) ◽  
pp. 95-107
Author(s):  
A. George Maria Selvam ◽  
Mary Jacintha ◽  
R. Dhineshbabu
Keyword(s):  
Stability Analysis ◽  
Boundary Value Problem ◽  
Fractional Order ◽  
Periodic Boundary ◽  
Boundary Value ◽  
Periodic Boundary Value Problem

On the existence of a solution for a periodic boundary value problem for semilinear fractional-order differential inclusions in Banach spaces

2021 ◽  
pp. 250-270
Author(s):  
Mikhail I. Kamenskii ◽  
Valeri V. Obukhovskii ◽  
Garik G. Petrosyan
Keyword(s):  
Boundary Value Problem ◽  
Fractional Order ◽  
Differential Inclusions ◽  
Periodic Boundary ◽  
Regularity Condition ◽  
Boundary Value ◽  
Continuous Functions ◽  
Periodic Boundary Value Problem ◽  
Existence Of A Solution ◽  
Measures Of Noncompactness

In this paper, we study a periodic boundary value problem for a class of semilinear differential inclusions of fractional order in a Banach space for which the multivalued nonlinearity satisfies the regularity condition expressed in terms of measures of noncompactness. To prove the existence of solutions to the problem, we first construct the corresponding Green function. Then we introduce into consideration a multivalued resolving operator in the space of continuous functions and reduce the posed problem to the existence of fixed points of the resolving multioperator. To prove the existence of a fixed point, a generalized theorem of B.N. Sadovskii type for a condensing multivalued map is used.

scholarly journals On a Periodic Boundary Value Problem for a Fractional–Order Semilinear Functional Differential Inclusions in a Banach Space

Mathematics ◽  
2019 ◽  
Vol 7 (12) ◽  
pp. 1146
Author(s):  
Mikhail Kamenski ◽  
Valeri Obukhovskii ◽  
Garik Petrosyan ◽  
Jen-Chih Yao
Keyword(s):  
Banach Space ◽  
Boundary Value Problem ◽  
Fractional Order ◽  
Periodic Boundary ◽  
Mild Solutions ◽  
Boundary Value ◽  
Periodic Boundary Value Problem ◽  
Diffusion Type ◽  
Result Theorem ◽  
Functional Differential

We consider the periodic boundary value problem (PBVP) for a semilinear fractional-order delayed functional differential inclusion in a Banach space. We introduce and study a multivalued integral operator whose fixed points coincide with mild solutions of our problem. On that base, we prove the main existence result (Theorem ). We present an example dealing with existence of a trajectory for a time-fractional diffusion type feedback control system with a delay satisfying periodic boundary value condition.

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