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

Advances in Nonlinear Analysis

article

Eduardo Cuesta¹  Mokhtar Kirane²  Ahmed Alsaedi³  Bashir Ahmad³ 

[1] Department Matematica Aplicada, Campus Miguel Delibes, University of Valladolid;Department of Mathematics, College of Art and Sciences, Khalifa University of Science and Technology, United Arab Emirates;Nonlinear Analysis and Applied Mathematics (NAAM)-Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University

关键词: Fractional derivative;    variable order;    regularity;    asymptotic behavior;   

DOI  :  10.1515/anona-2020-0182

学科分类：社会科学、人文和艺术（综合）

来源: De Gruyter

【 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】

CC BY