On the sub–diffusion fractional initial value problem with time variable order

Advances in Nonlinear Analysis

Cuesta Eduardo¹  Kirane Mokhtar²  Ahmad Bashir³  Alsaedi Ahmed³ 

[1] Department Matematica Aplicada, E.T.S.I. de Telecomunicacion, Campus Miguel Delibes, University of Valladolid, Paseo Belen 15, 47011Valladolid, Spain;Department of Mathematics, College of Art and Sciences, Khalifa University of Science and Technology, Abu Dhabi, United Arab Emirates;Nonlinear Analysis and Applied Mathematics (NAAM)-Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80257, Jeddah21589, Saudi Arabia;

关键词: fractional derivative;    variable order;    regularity;    asymptotic behavior;    34a08;    34d05;   

DOI  :  10.1515/anona-2020-0182

来源: DOAJ

【 摘 要 】

We consider a fractional derivative with order varying in time. Then, we derive for it a Leibniz' inequality and an integration by parts formula. We also study an initial value problem with our time variable order fractional derivative and present a regularity result for it, and a study on the asymptotic behavior.

【 授权许可】

Unknown