Surveys in Mathematics and its Applications

ISSN 1842-6298 (electronic), 1843-7265 (print)
 Volume 18 (2023), 83 -- 95

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CONFORMABLE FUNCTIONAL EVOLUTION EQUATIONS WITH NONLOCAL CONDITIONS IN BANACH SPACES

Abderrahmane Boukenkoul and Mohamed Ziane

Abstract. In this paper, we study semilinear conformable fractional evolution equations with finite delay subjected to nonlocal initial conditions in an arbitrary Banach space. We prove the existence of mild solutions under compactness type conditions on the nonlinear forcing term. Our result improves and complements several earlier related works. We apply our result to study a functional conformable partial differential equation of transport type.

2020 Mathematics Subject Classification: 26A33; 34A08; 47H08.
Keywords: conformable fractional derivative; mild solutions; measure of noncompactness.

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Abderrahmane Boukenkoul
Département d'Agronomie, Faculté des sciences de la vie et de l'environnement,
Université Abou Bekr Belkaid, Tlemcen 13000, Algérie.
e-mail: boukenkoula@gmail.com



Mohamed Ziane
Department of Mathematics,
Ibn Khaldoun University, Tiaret. Algeria.
e-mail: mohamed.ziane@univ-tiaret.dz

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