Harendra Singh (editor) - Methods of Mathematical Modelling: Fractional Differential Equations (Mathematics and its Applications)

Edited by Harendra Singh, Devendra Kumar and Dumitru Baleanu

Series Editor: Hemen Dutta

Department of Mathematics, Gauhati University

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Methods of Mathematical Modelling:
Fractional Differential Equations

Edited by Harendra Singh, Devendra Kumar, and Dumitru Baleanu

For more information about this series, please visit:

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Edited by Harendra Singh, Devendra Kumar and Dumitru Baleanu

Fractional Differential Equations

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Library of Congress Cataloging-in-Publication Data

Names: Singh, Harendra, editor. | Kumar, Devendra, editor. | Baleanu, D. (Dumitru), editor.

Title: Methods of mathematical modelling : fractional differential equations / edited by Harendra Singh, Devendra Kumar, and Dumitru Baleanu. Other titles: Methods of mathematical modelling (CRC Press)

Description: Boca Raton, FL : CRC Press/Taylor & Francis Group, 2019. | Summary: Mathematical modelling is a process which converts real-life problems into mathematical problems whose solutions make it easy to understand the real-life problem. Fractional modeling has many real-life applications in mathematics, science, and engineering. Such as viscoelasticity, chemical engineering, signal processing, bioengineering, control theory, and fluid mechanics. This book offers a collection of chapters on classical and modern dynamical systems modelled by fractional differential equations. This book will be useful to readers in increasing their knowledge in this field Provided by publisher. Identifiers: LCCN 2019020280 | ISBN 9780367220082 (hardback : acid-free paper) | ISBN 9780429274114 (ebook)

Subjects: LCSH: Mathematical models. | Fractional differential equations.

Classification: LCC TA342 .M43 2019 | DDC 515/.35dc23

LC record available at https://lccn.loc.gov/2019020280

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This book is planned for graduate students and researchers working in the area of mathematical modelling and fractional calculus. It describes several useful topics in mathematical modelling having real-life applications in chaos, physics, fluid mechanics and chemistry. The book consists of thirteen chapters and is organized as follows:

presents the dynamical behaviour of two ecosystems of three species consisting of prey, intermediate predator and top-predator that are still of current and recurring interests. The classical integer-order derivatives in such models are replaced with the AtanganaBaleanu fractional derivative in the sense of Caputo. Existence and uniqueness of solution are established. Linear stability analysis is examined in a view to guide the correct choice of parameters when numerically simulating the models. In the analysis, the condition for a dynamic system to be locally asymptotically stable is provided. A range of chaotic and spatiotemporal phenomena are obtained for different instances of [epsilon1] (0, 1) and are also given to justify the theoretical findings.

investigates the solutions for fractional diffusion equations subjected to reactive boundary conditions. For this, the system is defined in a semi-infinity medium, and the presence of a surface that may adsorb, desorb and/or absorb particles from the bulk is considered. The particles absorbed from the bulk by the surface may promote, by a reaction process, the formation of other particles. The particle dynamics is governed by generalized diffusion equations in the bulk and by kinetic equations on the surface; consequently, memory effects are taken into account in order to enable an anomalous diffusion approach and, consequently, non-Debye relaxations. The results exhibit a rich variety of behaviour for the particles, depending on the choice of characteristic times present in the boundary conditions or the fractional index present in modelling equations.

presents an efficient computational method for the approximate solution of the non-linear fractional Lienard equation (FLE), which describes the oscillating circuit. The Lienard equation is a generalization of the spring-mass system equation. The fractional derivative is in a LiouvilleCaputo sense. The computational method is a combination of collocation method and operational matrix method for Legendre scaling functions. Behaviour of solutions for different fractional order is shown through figures.