Fractional Stochastic Differential Equations

This book provides a thorough conversation on the underpinnings of Covid-19 spread modelling by using stochastics nonlocal differential and integral operators with singular and non-singular kernels. The book presents the dynamic of Covid-19 spread behaviour worldwide. It is noticed that the spread dynamic followed process with nonlocal behaviours which resemble power law, fading memory, crossover and stochastic behaviours. Fractional stochastic differential equations are therefore used to model spread behaviours in different parts of the worlds. The content coverage includes brief history of Covid-19 spread worldwide from December 2019 to September 2021, followed by statistical analysis of collected data for infected, death and recovery classes.

Presents an overview of COVID-19 spread by using non-local operators for modelling real-world problems Analyses the existence and uniqueness of solutions for stochasticfractional differential equations Explores new trends of numerical scheme for solving general stochasticfractional differential equations

Auteur

ABDON ATANGANA is Professor of Applied Mathematics at the University of the Free State (UFS), Bloemfontein, Republic of South Africa. He obtained his honours and master degrees from the Department of Applied Mathematics at the UFS with distinction. He obtained his Ph.D. in applied mathematics from the Institute for Groundwater Studies, UFS, Republic of South Africa. He serves as Editor of many international journals, Guest Editor of many journals, and is a reviewer of more than 200 international accredited journals. He has published more than 270 research papers in international accredited journals of applied mathematics, applied physics, geo-hydrology and biomathematics. A single author of four books, including Numerical Methods for Fractional Differentiation (Springer, 2019), he has graduated 7 Ph.D. and 22 graduate students and 6 postdoc fellows. His research interests are in methods and applications of partial and ordinary differential equations, fractional differential equations, perturbation methods, asymptotic methods, iterative methods, and groundwater modelling. Professor Atangana is the founder of "fractional calculus" with non-local and non-singular kernels popular in applied mathematics. A highly cited mathematician in 2019, 2020, 2021, he is the first-ever TWAS-Mohammad A award 2020 and Fellow of the World Academia of Science. SEDA IGRET ARAZ is Assistant Professor of Mathematics at Siirt University, Siirt, Turkey. She obtained her master and Ph.D. degrees from Ataturk University, Turkey. She is the author of more than 27 papers published in top-tier journals and a book, New Numerical Scheme with Newton Polynomial: Theory, Methods, and Applications, co-authored by Prof. Abdon Atangana. She has acted as guest editor on some special issues in several journals.

Résumé
"The book promotes the use of stochastic fractional differential models to describe infectious disease propagation, particularly the spread of COVID-19 ... . This is primary a research book, most of the results included therein being obtained by the authors themselves and presented for the first time in book form." (Paul Georgescu, zbMATH 1497.92002, 2022)

Contenu
History on Covid-19 Spread.- Fractional Dierential and Integral Operators.- Existence and Uniqueness for stochastic dierential equations.- Numerical scheme for a general Stochastic equation with classical and fractional derivatives.- A simple SIR model of Covid-19 spread.- An application of SEIRD approach.- Modelling the transmission of Coronavirus with SEIR approach.- Modeling the spread of Covid-19 with a SIA IR IU approach: Inclusion of unreported infected class.- A comprehensive analysis of Covid-19 model.- Analysis of SEIARD model of Coronavirus transmission.- A mathematical model with Covid-19 reservoir.- A new model with asymptomatic and quarantined classes.