1Department of Computer Science and Mathematics, Mouhamed Cherif Messadia University, Souk Ahras, Algeria
Acta mathematica Universitatis Comenianae, Tome 90 (2021) no. 3, pp. 277-288
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Ali Rezaiguia; Ali Rezaiguia. Existence results for q-fractional differential inclusions with non-convex right hand side. Acta mathematica Universitatis Comenianae, Tome 90 (2021) no. 3, pp. 277-288. http://geodesic.mathdoc.fr/item/AMUC_2021_90_3_a2/
@article{AMUC_2021_90_3_a2,
author = {Ali Rezaiguia and Ali Rezaiguia},
title = { Existence results for q-fractional differential inclusions with non-convex right hand side},
journal = {Acta mathematica Universitatis Comenianae},
pages = {277--288},
year = {2021},
volume = {90},
number = {3},
url = {http://geodesic.mathdoc.fr/item/AMUC_2021_90_3_a2/}
}
TY - JOUR
AU - Ali Rezaiguia
AU - Ali Rezaiguia
TI - Existence results for q-fractional differential inclusions with non-convex right hand side
JO - Acta mathematica Universitatis Comenianae
PY - 2021
SP - 277
EP - 288
VL - 90
IS - 3
UR - http://geodesic.mathdoc.fr/item/AMUC_2021_90_3_a2/
ID - AMUC_2021_90_3_a2
ER -
%0 Journal Article
%A Ali Rezaiguia
%A Ali Rezaiguia
%T Existence results for q-fractional differential inclusions with non-convex right hand side
%J Acta mathematica Universitatis Comenianae
%D 2021
%P 277-288
%V 90
%N 3
%U http://geodesic.mathdoc.fr/item/AMUC_2021_90_3_a2/
%F AMUC_2021_90_3_a2
In this paper, we investigate the solutions set for a $q$-fractional differential inclusion (1.1) $^{c}D_{q}^{\alpha }x(t) \in F ( t,x(t) , ^{c}D_{q}^{\alpha }x(t)), t\in [0,T]$, with the initial condition (1.2) $x(0) =x_{0}$ where $q \in (0,1) $ and $\alpha \in ( 0,1]$, $T>0$, $F: [0,T]\times \mathbb{R}\times \mathbb{R} \rightarrow \mathcal{P} (\mathbb{R}) $ is a multi-valued map. Our result is based on the fixed point theorem for multi-valued maps due to Covitz and Nadler. We also establish some Filippov's-type results for the problem (1.1)--(1.2). Finally, an example is presented to illustrate our main results.
