Solvability of A Solution and Controllability for Nonlinear Fractional Differential Equations
by
Rezzoug Imad
Oussaeif Taki-Eddine
Benbrahim Abdelouahab
Vol. 15 No. 3 (2020) P.237~P.249
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DOI: | https://doi.org/10.21915/BIMAS.2020303 |
| | 10.21915/BIMAS.2020303 |
ABSTRACT
In this paper, we establish the existence and uniqueness of solutions for a nonlinear fractional differential equation with nonlocal boundary conditions. We employ Schauder fixed point theorem to study the existence of a solution of the problem. We also use the Banach fixed point theorem to study the existence of a unique solution. Finally, we
provide examples to illustrate our results. Thus, we study the null-controllability for the fractional differential equation with constraints on the control. The main tool used to solve the problem of existence and convergence is an observability inequality of Carleman type, which is “adapted” to the constraints. We then apply the obtained results to the sentinels theory of Lions.
KEYWORDS
Fractional di erential equations, Caputo fractional derivative, xed point theorem, Null-controllability, Inequality of Carleman, Sentinels theory
MATHEMATICAL SUBJECT CLASSIFICATION 2010
Primary: 34K37; 34A08; 34A34; 58C30; 34A12; 93B05; 49J20
MILESTONES
Received: 2020-02-12
Revised : 2020-09-13
Accepted: 2020-09-13
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