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Lie Symmetry Analysis of Fractional Differential Equations



ISBN 9780367441869
Published July 10, 2020 by Chapman and Hall/CRC
222 Pages

 
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Book Description

The trajectory of fractional calculus has undergone several periods of intensive development, both in pure and applied sciences. During the last few decades fractional calculus has also been associated with the power law effects and its various applications.

It is a natural to ask if fractional calculus, as a nonlocal calculus, can produce new results within the well-established field of Lie symmetries and their applications.

In Lie Symmetry Analysis of Fractional Differential Equations the authors try to answer this vital question by analyzing different aspects of fractional Lie symmetries and related conservation laws. Finding the exact solutions of a given fractional partial differential equation is not an easy task, but is one that the authors seek to grapple with here. The book also includes generalization of Lie symmetries for fractional integro differential equations.

Features

  • Provides a solid basis for understanding fractional calculus, before going on to explore in detail Lie Symmetries and their applications
  • Useful for PhD and postdoc graduates, as well as for all mathematicians and applied researchers who use the powerful concept of Lie symmetries
  • Filled with various examples to aid understanding of the topics

Table of Contents

Chapter 1: Lie symmetry analysis of integer order differential equations. 

Chapter 2: Group analysis and exact solutions of fractional partial differential. 

Chapter 3: Analytical lie group approach for solving the fractional integro-differential equations. 

Chapter 4: Nonclassical Lie symmetry analysis to fractional differential equations. 

Chapter 5: Conservation laws of the fractional differential equations.

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Author(s)

Biography

Mir Sajjad Hashemi is associate professor at the University of Bonab, Iran. His field of interests include the fractional differential equations, Lie symmetry method, Geometric integration, Approximate and analytical solutions of differential equations and soliton theory.

Dumitru Baleanu is professor at the Institute of Space Sciences, Magurele-Bucharest, Romania and visiting staff member at the Department of Mathematics, Cankaya University, Ankara, Turkey. His field of interests include  the fractional dynamics and its applications in science and engineering, fractional differential equations, discrete mathematics, mathematical physics, soliton theory, Lie symmetry, dynamic systems on time scales and the wavelet method and its applications. 

Reviews

"Written by top experts in the field, this book is a modern and comprehensive approach to the Lie Symmetry groups, guiding the reader along the tortuous path through the theory of fractional differential operators".

— Carlo Cattani, University of Tuscia

"This book is the first to apply Lie symmetry analysis to fractional differential equations. Read this book and learn from one of the best."

—Elyas Shivanian, Imam Khomeini International University