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Existence results for impulsive semilinear fractional differential inclusions with delay in Banach spaces

Hammouche Hadda;  Guerbati Kaddour;  Benchohra Mouffak;  Abada Nadjat — 2013

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

In this paper, we introduce a new concept of mild solution of some class of semilinear fractional differential inclusions of order 0 < α < 1. Also we establish an existence result when the multivalued function has convex values. The result is obtained upon the nonlinear alternative of Leray-Schauder type.

On the radius of spatial analyticity for the higher order nonlinear dispersive equation

Aissa Boukarou;  Kaddour Guerbati;  Khaled Zennir — 2022

Mathematica Bohemica

In this work, using bilinear estimates in Bourgain type spaces, we prove the local existence of a solution to a higher order nonlinear dispersive equation on the line for analytic initial data u 0 . The analytic initial data can be extended as holomorphic functions in a strip around the x -axis. By Gevrey approximate conservation law, we prove the existence of the global solutions, which improve earlier results of Z. Zhang, Z. Liu, M. Sun, S. Li, (2019).

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