@article{2eb324ae92b44657bcfb07cc090ccb6c,
title = "On the sub-diffusion fractional initial value problem with time variable order",
abstract = "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.",
keywords = "asymptotic behavior, Fractional derivative, regularity, variable order",
author = "Eduardo Cuesta and Mokhtar Kirane and Ahmed Alsaedi and Bashir Ahmad",
note = "Funding Information: This project was funded by the Deanship of Scientific Research (DSR) at King Abdulaziz University, Jeddah, under grant no. (RG-42-130-41). The authors, therefore, acknowledge with thanks DSR technical and financial support. Funding Information: E. Cuesta was supported by Spanish Ministerio de Econom{\'i}a y Compteitividad under the Research Grant RTI2018-094569-B100. Funding Information: This project was funded by the Deanship of Scientific Research (DSR) at King Abdulaziz University, Jeddah, under grant no. (RG-42-130-41). The authors, therefore, acknowledge with thanks DSR technical and financial support. E. Cuesta was supported by Spanish Ministerio de Economia y Compteitividad under the Research Grant RTI2018-094569-B100. E. Cuesta was supported by Spanish Ministerio de Economia y Compteitividad under the Research Grant RTI2018-094569-B100. Publisher Copyright: {\textcopyright} 2021 Eduardo Cuesta et al., published by De Gruyter 2021.",
year = "2021",
month = jan,
day = "1",
doi = "10.1515/anona-2020-0182",
language = "British English",
volume = "10",
pages = "1301--1315",
journal = "Advances in Nonlinear Analysis",
issn = "2191-9496",
publisher = "De Gruyter Open Ltd.",
number = "1",
}