Fractional Differential Equations and Inclusions: Classical and Advanced Topics

This monograph is devoted to the existence and stability (Ulam–Hyers–Rassias stability and asymptotic stability) of solutions for various classes of functional differential equations or inclusions involving the Hadamard or Hilfer fractional derivative. Some equations present delay which may be finite, infinite, or state-dependent. Others are subject to impulsive effect which may be fixed or non-instantaneous. Readers will find the book self-contained and unified in presentation. It provides the necessary background material required to go further into the subject and explores the rich research literature in detail. Each chapter concludes with a section devoted to notes and bibliographical remarks and all abstract results are illustrated by examples. The tools used include many classical and modern nonlinear analysis methods such as fixed-point theorems, as well as some notions of Ulam stability, attractivity and the measure of non-compactness as well as the measure of weak noncompactness. It is useful for researchers and graduate students for research, seminars, and advanced graduate courses, in pure and applied mathematics, physics, mechanics, engineering, biology, and all other applied sciences.

Dr Mouffak Benchohra is a Full Professor at the department of mathematics, Djillali Liabes University of Sidi Bel Abbes since October 1994. Benchohra received the master's degree in Nonlinear Analysis from Tlemcen University, Algeria, 1994 and Ph.D. degree in Mathematics from Djillali Liabes University, Sidi Bel Abbes, Algeria. His research fields include fractional differential equations, evolution equations and inclusions, control theory and applications, etc. Benchohra has published more than 500 papers, and five monographs. He is a Highly Cited Researcher in Mathematics from Thompson Reuters (2014) and Clarivate Analytics (2017–2018). Benchohra has also occupied the position of head of department of mathematics at Djillali Liabes University, Sidi Bel Abbes. He is in the Editorial Board of 10 international journals.

Dr Jamal Eddine Lazreg is an Associate Professor at the department of mathematics, Djillali Liabes University of Sidi Bel Abbes since 2016. Lazreg received the master's degree in functional analysis from Djillali Liabes University, Algeria, 2009, and the doctorate's degree in differential equations from Djillali Liabes University of Sidi Bel Abbes, Algeria, 2014. His research fields include fractional differential equations and inclusions.

Dr Juan José Nieto is a Spanish mathematician, who has been a Professor of Mathematical Analysis at the University of Santiago de Compostela since 1991. Nieto received his degree in Mathematics from the University of Santiago de Compostela in 1980. He was then awarded a Fulbright scholarship and moved to the University of Texas at Arlington where he worked with Professor V Lakshmikantham. He received his PhD in Mathematics from the University of Santiago de Compostela in 1983. Nieto's research interests include differential equations, fractional calculus, fuzzy equations and epidemiological models. He is one of the world's most cited mathematicians according to Web of Knowledge, and appears in the Thompson Reuters Highly Cited Researchers list. Nieto has also occupied different positions at the University of Santiago de Compostela, such as Dean of Mathematics and Director of the Mathematical Institute. He was the editor-in-chief of the journal Nonlinear Analysis: Real World Applications from 2009 to 2012. Additionally, he has worked as an editor for the Journal of Mathematics Analysis and Applications, the International Journal of Biomathematics, and the Journal of The Franklin Institute, as well as numerous others. In 2016, Nieto was admitted as a Fellow of the Royal Galician Academy of Sciences.

Dr Yong Zhou is a Full Professor of Faculty of Mathematics and Computational Science at Xiangtan University since August 2000. He is also a Distinguished Guest Professor of Macau University of Science and Technology since 2018, and Distinguished Adjunct Professor of King Abdulaziz University since 2015. His research fields include fractional differential equations, evolution equations and inclusions, control theory. Zhou has published five monographs with Springer, Elsevier, De Gruyter, World Scientific and Science Press, respectively, and more than 300 research papers in international journals. He appears in the Highly Cited Researchers list from Thompson Reuters (2014) and Clarivate Analytics (2015–2021). Zhou has undertaken five projects from National Natural Science Foundation of China, and one project of the Fundo para o Desenvolvimento das Ciencias e da Tecnologia from the Macau Special Administrative Region of China. He was the Editor-in-Chief of International Journal of Dynamical Systems and Differential Equations from 2007 to 2011. In addition, he had worked as an Associate Editor for IEEE Transactions on Fuzzy Systems.