Surveys in Mathematics and its Applications

ISSN 1842-6298 (electronic), 1843-7265 (print)
 Volume 14 (2019), 307 -- 325

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NONLOCAL FRACTIONAL DIFFERENTIAL INCLUSIONS WITH IMPULSES AT VARIABLE TIMES

Abdelghani Ouahab and Sarah Seghiri

Abstract. In this paper, we study the existence of mild solutions for a fractional semi-linear differential inclusions posed in a Banach space with nonlocal conditions and impulses at variable times. The main existence result is obtained by using fractional calculus, measure of noncompactness, and multivalued fixed point theory. We study also the topological properties of the solution set.

2010 Mathematics Subject Classification: 47H10; 26A33; 34A60; 34B37; 14F45.
Keywords: Fixed point theorems; Fractional derivatives; Differential inclusions; Boundary value problems with impulses; Topological properties.

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Abdelghani Ouahab
Department of Mathematics and Informatics,
The African University Ahmed Draia of Adrar,
Adrar, Algeria.
e-mail: agh_ouahab@univ-adrar.dz
and
Laboratory of Mathematics,
Sidi-Bel-Abbès University,
PoBox 89, 22000 Sidi-Bel-Abbès, Algeria.
  
Sarah Seghiri
Departement of Mathematics,
Normal High School,
B.P N 92, Vieux Kouba, Algiers,
Algeria.
e-mail: saramer29@live.com
and
Laboratory of Fixed Point Theory and Its Applications,
Normal High School,
B.P N 92, Vieux Kouba, Algiers,
Algeria.

http://www.utgjiu.ro/math/sma