Fractional Differential Equations
Theoretical Aspects and Applications
- 1st Edition - April 29, 2024
- Imprint: Academic Press
- Editors: Praveen Agarwal, Carlo Cattani, Shaher Momani
- Language: English
- Paperback ISBN:9 7 8 - 0 - 4 4 3 - 1 5 4 2 3 - 2
- eBook ISBN:9 7 8 - 0 - 4 4 3 - 1 5 4 2 4 - 9
Fractional Differential Equations: Theoretical Aspects and Applications presents the latest mathematical and conceptual developments in the field of Fractional Calculus and explor… Read more
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Request a sales quoteFractional Differential Equations: Theoretical Aspects and Applications presents the latest mathematical and conceptual developments in the field of Fractional Calculus and explores the scope of applications in research science and computational modeling. The book delves into these methods and applied computational modelling techniques, including analysis of equations involving fractional derivatives, fractional derivatives and the wave equation, analysis of FDE on groups, direct and inverse problems, functional inequalities, and computational methods for FDEs in physics and engineering. Other modeling techniques and applications explored include general fractional derivatives involving the special functions in analysis and fractional derivatives with respect to other functions. Fractional Calculus, the field of mathematics dealing with operators of differentiation and integration of arbitrary real or even complex order, extends many of the modelling capabilities of conventional calculus and integer-order differential equations and finds its application in various scientific areas, such as physics, mechanics, engineering, economics, finance, biology, and chemistry, among others.
- Provides the most recent and up-to-date developments in the theory and scientific applications Fractional Differential Equations
- Includes transportable computer source codes for readers in MATLAB, with code descriptions as it relates to the mathematical modelling and applications
- Provides readers with a comprehensive foundational reference for this key topic in computational modeling, which is a mathematical underpinning for most areas of scientific and engineering research
Mathematicians, researchers in computational modelling and computational biology, computer scientists, engineers, as well as researchers in biomedical engineering, control engineering, mechatronics, and robotics
- Cover image
- Title page
- Table of Contents
- Copyright
- Contributors
- Chapter 1: Extension of the truncated M-fractional derivative linked to multivariate generalized Mittag-Leffler function demonstrating classical characteristics
- Abstract
- 1.1. Introduction
- 1.2. Preliminaries
- 1.3. Truncated M-fractional derivative
- 1.4. Generalized M-integral
- 1.5. Relation with other fractional derivatives
- 1.6. Conclusion
- References
- Chapter 2: A generalization of the Apostol-type Frobenius–Genocchi polynomials of level ι
- Abstract
- 2.1. Introduction
- 2.2. Background and previous results
- 2.3. The generalized Apostol-type Frobenius–Genocchi polynomials of level ι and their properties
- References
- Chapter 3: Certain properties of generalized Mittag-Leffler operators
- Abstract
- Acknowledgements
- 3.1. Introduction
- 3.2. Moment estimates
- 3.3. Rate of convergence
- 3.4. Rate of convergence in Lipschitz-type spaces
- 3.5. A-statistical convergence
- 3.6. λγ-statistical convergence
- References
- Chapter 4: Differential operational techniques and applications
- Abstract
- 4.1. Introduction
- 4.2. Properties of differential operators
- 4.3. Applications
- 4.4. Conflict of interest
- References
- Chapter 5: Some results on Wright function
- Abstract
- Acknowledgement
- 5.1. Introduction and preliminaries
- 5.2. Integral representations of Wright function
- 5.3. Relations with other special functions
- References
- Chapter 6: Computational methods for the fractional differential equations in physics and engineering
- Abstract
- 6.1. Introduction
- 6.2. Spline function methods and solutions of linear and nonlinear fractional differential equations
- 6.3. Spline approximation method for a system of fractional differential equations
- 6.4. Modified homotopy perturbation method for the fractional Bagley–Torvik equation
- 6.5. Conclusion
- References
- Chapter 7: A study on the properties of new generalized special functions, their integral transformations, and applications to fractional differential equations
- Abstract
- 7.1. Introduction and preliminaries
- 7.2. New generalized special functions
- 7.3. Properties
- 7.4. Integral transforms
- 7.5. Solution of fractional differential equations
- 7.6. Conclusion
- References
- Chapter 8: Congruence between mild and classical solutions of generalized fractional impulsive evolution equation
- Abstract
- 8.1. Introduction and preliminaries
- 8.2. Mild solution
- 8.3. Classical solution
- 8.4. Congruence between classical and mild solutions
- References
- Chapter 9: Application of various methods to solve some fractional differential equations in different fields
- Abstract
- 9.1. Introduction
- 9.2. Preliminaries
- 9.3. Idea of the used methods
- 9.4. Results and discussion
- 9.5. Conclusion
- References
- Chapter 10: Modeling capillary absorption in building materials with emphasis on the fourth root time law: time-fractional models, solutions, and analysis
- Abstract
- Acknowledgements
- 10.1. Introduction
- 10.2. New approach: physical and modeling background
- 10.3. Next study tasks
- 10.4. A variety of alternative models
- 10.5. Some briefs and preliminarily analyses
- 10.6. Tests with published data: does the 1/4 law is obeyed everywhere?
- 10.7. Concentration profiles: approximate solutions
- 10.8. The parameter m and the exponent n in the nonlinear diffusion model: some suggestions
- 10.9. Conclusions
- References
- Chapter 11: Fuzzy fractional Caputo-type numerical scheme for solving fuzzy nonlinear equations
- Abstract
- 11.1. Introduction
- 11.2. Construction of fuzzy fractional Newton-type numerical schemes
- 11.3. Numerical results
- 11.4. Conclusion
- References
- Chapter 12: Approximate solutions of epidemic model of Zika virus
- Abstract
- 12.1. Introduction
- 12.2. Preliminaries on fractional calculus
- 12.3. Mathematical model formulation
- 12.4. Basic properties of the model
- 12.5. Analysis
- 12.6. Numerical methods and simulations
- 12.7. Numerical simulation and sensitivity analysis
- 12.8. Convergence analysis
- 12.9. Discussion
- 12.10. Conclusion
- References
- Chapter 13: On the nonlocal boundary value problem for the coupled system
- Abstract
- 13.1. Introduction
- 13.2. Existence of solution
- 13.3. Uniqueness of solution
- 13.4. Continuous dependence
- 13.5. Both analytical and numerical approaches
- 13.6. Numerical examples
- 13.7. Conclusion
- References
- Chapter 14: Solutions of nonlinear time fractional Klein–Gordon equations using composite fractional derivatives
- Abstract
- 14.1. Introduction
- 14.2. Basic tools
- 14.3. Solution of nonlinear fractional Klein–Gordon equations with composite fractional derivatives
- 14.4. Applications
- 14.5. Conclusion
- References
- Chapter 15: Some generating functions for I-function
- Abstract
- 15.1. Introduction and preliminaries
- 15.2. Main results
- References
- Chapter 16: Approximate solution to the KdV equation in superthermal plasmas
- Abstract
- 16.1. Introduction
- 16.2. Governing equations
- 16.3. Nonlinear analysis
- 16.4. Basic idea of ADM
- 16.5. ADM approach to KdV
- 16.6. Results and discussions
- 16.7. Conclusions
- References
- Chapter 17: Turán-type inequalities for generalized fractional operators and special functions
- Abstract
- Acknowledgements
- 17.1. Introduction
- 17.2. Preliminaries
- 17.3. Turán-type inequality of k-fractional integral operators
- 17.4. Turán-type inequality for generalized Caputo-type k-fractional operator
- 17.5. Turán-type inequalities for extended hypergeometric functions
- References
- Index
- Edition: 1
- Published: April 29, 2024
- Imprint: Academic Press
- No. of pages: 270
- Language: English
- Paperback ISBN: 9780443154232
- eBook ISBN: 9780443154249
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Praveen Agarwal
Dr. Praveen Agarwal is Vice-Principal and Professor at Anand International College of Engineering, Jaipur, India. He is listed as the World's Top 2% Scientist in 2020, 2021, 2022, and 2023, released by Stanford University. In the 2023 ranking of best scientists worldwide announced by Research.com, he ranked 21st at the India level and 2436th worldwide in Mathematics. He is a Managing Editor of Book seriesMathematics for Sustainable Developments, Springer Nature,and Editor ofBook series Mathematical Modelling & Computational Method for Innovation, Taylor & Francis Group.
He published more than 350 papers in international reputed Journals.
Affiliations and expertise
Full Professor, Anand International College of Engineering, Jaipur India; Nonlinear DynamicsResearch Center (NDRC), Ajman University, Ajman, UAE; Peoples Friendship University of Russia (RUDN University), Russian FederationCC
Carlo Cattani
Dr. Carlo Cattani is Full Professor of Mathematical Physics and Applied Mathematics at the Department of Economics, Engineering, Society and Enterprise (DEIM) at Università degli Studi della Tuscia, Viterbo, Italy. He has been previously appointed as Professor and Research Fellow at the Department of Mathematics, University of Rome La Sapienza, and Department of Mathematics, University of Salerno. Dr. Cattani has been a Research Fellow at the Italian Council of Research (CNR) and Visiting Research Fellow at the Physics Institute of Stockholm University. His main scientific research interests are focused on numerical and computational methods, mathematical models and methods, time series and data analysis, computer methods and simulations. Dr. Cattani is co-author of several books, including The Natural Language for Artificial Intelligence, Elsevier Academic Press; Wavelet and Wave Analysis as Applied to Materials with Micro or Nanostructure, World Scientific Publishing; Fractional Dynamics, De Gruyter; Computational Methods for Data Analysis, De Gruyter; Fractal Analysis: Basic Concepts and Applications, World Scientific Publishing; Symmetry and Complexity, Mdpi AG; and Advances in Mathematical Modelling: Applied Analysis and Computation, Springer. He has made significant contributions to scientific and mathematical research on fundamental topics such as numerical methods, dynamical systems, fractional calculus, fractals, wavelets, nonlinear waves, and data analysis. Dr. Cattani is Editor in Chief of the journals Fractal and Fractional and Information Sciences Letters.
Affiliations and expertise
Professor (habil. full professor) of Mathematical Physics and Applied Mathematics at the Engineering School (DEIM) of Tuscia University (VT), ItalySM
Shaher Momani
Dr. Shaher Momani is Dean of the College of Humanities and Sciences at Ajman University, United Arab Emirates, and Distinguished Professor of Mathematics at the University of Jordan. He has previously been Dean of Scientific Research, Dean of Faculty of Science, and Head of Department of Mathematics at The University of Jordan. Dr. Momani has received numerous academic honors in the course of his career, including among many others The Order of King Abdullah II Ibn Al Hussein for Academic Contributions in Scientific Research, Jordanian Star of Science, ISI Web of Science Highly-Cited Interdisciplinary Researcher, ISI Web of Science Highly-Cited Researcher in Mathematics, named by Clarivate Analytics as one of the World’s Most Influential Scientific Minds 2014-2018, Liouville Award for Lifetime Achievement in Fractional Calculus, and the Mittag-Leffler Award for Fractional Differentiation and Its Applications. Dr. Momani has been classified as the top scientist in the world in terms of publications in fractional differential equations according to Clarivate and Scopus from 2008-2015, currently with 6959 Scopus citations. Dr. Momani is Editor in Chief of Numerical and Computational Methods in Sciences and Engineering. His research interests include Mathematical Modelling, Fractional Dynamical Systems, Numerical solution of ordinary and partial differential equations of fractional order, theory of fractional differential equations and integral equations, Newtonian and non-Newtonian fluid dynamics, stability of fractional linear systems, fractional order modelling and control in Biomedical Engineering, variational inequalities and obstacle problems, Mathematical Biology, and Mathematical Physics.
Affiliations and expertise
Dean, College of Humanities and Sciences, Ajman University, United Arab Emirates and Distinguished Professor of Mathematics, University of Jordan, JordanRead Fractional Differential Equations on ScienceDirect