Modeling of Discrete and Continuous Systems Ordinary, Partial and Fractional Derivatives

This book contains a comprehensive collection of chapters on recent and original research, along with review articles, on mathematical modeling of dynamical systems described by various types of differential equations. Structured into 18 chapters dedicated to exploring different aspects of differential equations and their applications in modeling both discrete and continuous systems, it highlights theoretical advancements in mathematics and their practical applications in modeling dynamic systems. Readers will find contributions by renowned scholars who delve into the intricacies of nonlinear dynamics, stochastic processes, and partial differential equations. This book is an essential resource for researchers, academicians, and practitioners in the field of mathematical modeling.

Chapter 1 Fractional Differential Equations in Engineering Sciences.- Chapter 2 A New Operator Approach for Solving Time-Fractional Nonlinear Burgess Equation.- Chapter 3 Explicit Formulas for the Solutions of a Solvable.- Chapter 4 Stochastic Equations with Deviating Argument Driven by Poisson Jumps.- Chapter 5 A Review on Fractional Calculus in Modelling of Cancer.

Mohamed Kharrat is Associate Professor at the College of Science, Jouf University, Associate Professor at Sfax University and a member of the Research Laboratory of Probability and Statistics, Faculty of Sciences, University of Sfax, Tunisia. He received his Ph.D. and Habilitation degrees in mathematics from the University of Sfax, Tunisia, in 2014 and 2021, respectively. With more than 35 papers published in reputed journals and books, he has been serving as Reviewer and a Board Member for several journals. His main research interests include stochastic differential equations, fractional differential equations, nonlinear systems, mathematical finance, adaptive control, and the study of stability.

Nouressadat Touafek is Full Professor of Mathematics at Mohamed Seddik Ben Yahia University, Jijel, Algeria. He received his M.Sc. (in numerical analysis) and Ph.D. (in pure mathematics) degrees from Constantine University, Algeria. With more than 45 papers in different reputed journals, he has been Supervisor of 5 Ph.D. theses and 8 M.Sc. theses, and a referee for many journals. Editor of the Palestine Journal of Mathematics journal and the Journal of Innovative Applied Mathematics and the Computational Sciences journal, his research interests include finite elements method, elliptic curves, Mahler measure, and difference equations.

Moez Krichen is Associate Professor of Computer Science at Al Baha University, Saudi Arabia and a member of the Research Laboratory on Development and Control of Distributed Applications, University of Sfax, Sfax, Tunisia. He received his Ph.D. degree in computer science from Joseph Fourier University, Grenoble, France, in 2007, and the HDR (Ability to Conduct Research) degree in computer science from the University of Sfax, Sfax, Tunisia, in 2018. Currently, he is working on formal aspects related to deep learning, data mining, blockchain, smart contracts, and optimization. His main research interests include model-based conformance, load, and security testing methodologies for real-time, distributed, and dynamically adaptable systems. In addition, he works on applying formal methods to several modern technologies like smart cities, the Internet of Things, smart vehicles, drones, and healthcare systems.