Recent Trends in Fractional Calculus and Its Applications
- 1st Edition - July 2, 2024
- Editors: Praveen Agarwal, Luis Vázquez Martínez, Ervin K. Lenzi
- Language: English
- Paperback ISBN:9 7 8 - 0 - 4 4 3 - 1 8 5 0 5 - 2
- eBook ISBN:9 7 8 - 0 - 4 4 3 - 1 8 5 0 6 - 9
Recent Trends in Fractional Calculus and Its Applications addresses the answer to this very basic question: "Why is Fractional Calculus important?" Until recent times, Fractiona… Read more
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Request a sales quoteRecent Trends in Fractional Calculus and Its Applications addresses the answer to this very basic question: "Why is Fractional Calculus important?" Until recent times, Fractional Calculus was considered as a rather esoteric mathematical theory without applications, but in the last few decades there has been an explosion of research activities on the application of Fractional Calculus to very diverse scientific fields ranging from the physics of diffusion and advection phenomena, to control systems to finance and economics. An important part of mathematical modelling of objects and processes is a description of their dynamics.
The term Fractional Calculus is more than 300 years old. It is a generalization of the ordinary differentiation and integration to noninteger (arbitrary) order. The subject is as old as the calculus of differentiation and goes back to times when Leibniz, Gauss, and Newton invented this kind of calculation. Several mathematicians contributed to this subject over the years. People like Liouville, Riemann, and Weyl made major contributions to the theory of Fractional Calculus. In recent decades the field of Fractional Calculus has attracted the interest of researchers in several areas, including mathematics, physics, chemistry, engineering, finance, and social sciences.
The term Fractional Calculus is more than 300 years old. It is a generalization of the ordinary differentiation and integration to noninteger (arbitrary) order. The subject is as old as the calculus of differentiation and goes back to times when Leibniz, Gauss, and Newton invented this kind of calculation. Several mathematicians contributed to this subject over the years. People like Liouville, Riemann, and Weyl made major contributions to the theory of Fractional Calculus. In recent decades the field of Fractional Calculus has attracted the interest of researchers in several areas, including mathematics, physics, chemistry, engineering, finance, and social sciences.
- Provides the most recent and up-to-date developments in the Fractional Calculus and its application areas
- Presents pre-preparation ideas to help researchers/scientists/clinicians face the new challenges in the application of fractional differential equations
- Helps researchers and scientists understand the importance of the Fractional Calculus to solve many problems in Biomedical Engineering and applied sciences
Mathematicians, Computer Scientists, and researchers in computational modelling and computational biology, researchers and clinicians in Biomedical Engineering and medical imaging. Other interested audiences will be comprised of radiologists, neurologists, cardiologists, AI researchers, and designers of Machine Learning applications, Clinicians and researchers interested in a variety of Engineering and other scientific research applications
- Cover image
- Title page
- Table of Contents
- Copyright
- List of contributors
- 1: On generalized Dirichlet averages and fractional calculus
- Abstract
- 1.1. Introduction
- 1.2. Dirichlet averages
- 1.3. Generalized Dirichlet averages
- 1.4. Modified type-1 Dirichlet measure and Dirichlet averages
- 1.5. Isotropic random points
- 1.6. Fractional integral operators with many variables and statistical distributions
- 1.7. Dirichlet average of generalized Mittag-Leffler function via pathway fractional integral
- 1.8. Conclusions
- References
- 2: Generalizations of some important fractional integral inequalities by using a parameter
- Abstract
- 2.1. Introduction
- 2.2. An identity for twice differentiable functions
- 2.3. Parameterized inequalities for generalized fractional integrals
- 2.4. Conclusions
- References
- 3: Elzaki transform of pathway fractional integral formulae involving extended k-hypergeometric functions
- Abstract
- 3.1. Introduction and preliminaries
- 3.2. Main results
- 3.3. Particular cases
- 3.4. Conclusions
- References
- 4: Application of fractional-order Fibonacci wavelets to solve variable-order fractional partial differential equations
- Abstract
- 4.1. Introduction
- 4.2. Definitions and preliminaries
- 4.3. Fractional-order Fibonacci wavelets
- 4.4. New achievements
- 4.5. Description of the computational method
- 4.6. Convergence analysis
- 4.7. Numerical experiments
- 4.8. Conclusions
- References
- 5: Optimization of the approximate solution of the fractional squeezing flow between two infinite plates
- Abstract
- 5.1. Introduction
- 5.2. Mathematical formulation of the problem
- 5.3. Constructing a new family of basis functions
- 5.4. Description of the method
- 5.5. Convergence analysis of the method
- 5.6. Numerical results
- 5.7. Conclusions
- Conflict of interest
- References
- 6: Multi-parameter generalized fractional operators and their integral transforms
- Abstract
- 6.1. Introduction
- 6.2. Basic concepts
- 6.3. Multi-parameter generalized fractional operators
- 6.4. Examples
- 6.5. Conclusions
- References
- 7: A constructive approach to the fractional Zakharov–Kuznetsov equations of weak nonlinear acoustic ion waves in plasma
- Abstract
- 7.1. Introduction
- 7.2. Preamble
- 7.3. Convergence and error analysis: NITHPM
- 7.4. Constructive approach: NITHPM
- 7.5. Application of NITHPM
- 7.6. Graphical result and analysis
- 7.7. Conclusions
- References
- 8: Integral formula for matrix factorizations of Helmholtz equation
- Abstract
- 8.1. Introduction
- 8.2. Materials and methods
- Declarations
- References
- 9: Cauchy problem for matrix factorizations of Helmholtz equation on a plane
- Abstract
- 9.1. Introduction
- 9.2. The Cauchy problem for matrix factorizations of Helmholtz equation in a two-dimensional bounded domain
- Declarations
- References
- 10: The Cauchy problem for matrix factorizations of Helmholtz equation in space
- Abstract
- 10.1. Introduction
- 10.2. The Cauchy problem for matrix factorizations of the Helmholtz equation in a three-dimensional bounded domain
- 10.3. Integral formula in the layer-type region
- 10.4. Regularization of the Cauchy problem for matrix factorizations of the Helmholtz equation in a layer-type domain
- Declarations
- References
- 11: Modified Newton successive over-relaxation for solving Caputo fractional porous medium equations
- Abstract
- 11.1. Introduction
- 11.2. Time-fractional porous medium equation in Caputo sense
- 11.3. Iterative method and algorithm
- 11.4. Numerical experiment, results, and discussions
- 11.5. Conclusions
- References
- 12: Fractional calculi on time scales: differentiation and integration of a function with respect to another function
- Abstract
- Acknowledgement
- 12.1. Introduction
- 12.2. Preliminaries on time scales
- 12.3. Fractional calculus on time scales of a function with respect to another function
- References
- 13: Effective strategies to reduce transmission of certain diseases based on their fractional optimal control problems
- Abstract
- 13.1. Introduction
- 13.2. Preliminaries
- 13.3. Results and discussion
- 13.4. Conclusions
- References
- 14: Fractional Caputo-type simultaneous scheme for finding all polynomial roots
- Abstract
- 14.1. Introduction
- 14.2. Construction of fractional-type family of numerical scheme
- 14.3. Dynamical analysis
- 14.4. Numerical results
- 14.5. Conclusions
- References
- 15: Application of modified homotopy analysis transform method to fractional modified Kawahara equation
- Abstract
- Acknowledgements
- 15.1. Introduction
- 15.2. Basic definitions
- 15.3. Novel modified homotopy analysis transform method
- 15.4. Numerical analysis of fractional Kawahara equation using MHATM
- 15.5. Numerical result and discussion
- 15.6. Conclusions
- Funding
- Availability of data and materials
- Conflict of interest
- Authors' contribution
- References
- Index
- No. of pages: 320
- Language: English
- Edition: 1
- Published: July 2, 2024
- Imprint: Academic Press
- Paperback ISBN: 9780443185052
- eBook ISBN: 9780443185069
PA
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 FederationLM
Luis Vázquez Martínez
Dr. Luis Vázquez Martínez is Professor Emeritus of Applied Mathematics Departamento de Matématica Aplicada, Faculdad do Informática, Universidad Complutense de Madrid, Spain. Dr. Martínez has held many distinguished administrative positions throughout his career, including Vice-Dean of Research, External Relations and Students of Facultad de Ciencias Físicas, Academic Director of Research at UCM, and Director and Founder of the European Office of Research and the Supercomputing Center, UCM, among many others. Dr. Martínez has received many awards and research honors during his distinguished career, including the Daza Valdés Prize from the Spanish Society of Optica, Cavaliere dell’Ordine della Stella from the Republic of Italy, NASA Distinction as Principal Investigator of REMS-Curiosity-MSL, and the Liouville Award for Lifetime Achievements in the Area of Fractional Calculus and Its Applications. Dr. Martínez was a Founding Member of the Centre of Astrobiology associated with NASA in its Mars exploration program, where he founded and managed the Advanced Computer Laboratory.
Affiliations and expertise
Professor Emeritus of Applied Mathematics Departamento de Matématica Aplicada, Faculdad do Informática, Universidad Complutense de Madrid, SpainEL
Ervin K. Lenzi
Dr. Ervin K. Lenzi is Associate Professor of Physics at Universidade Estaudal de Ponta Grossa, Brazil. Dr. Lenzi has a Ph.D. in Physics from Centro Brasileiro de Pesquisas Física, and was a Postdoc Fellow in Physics at Politecnico di Torino, Italy. His research interests include Diffusive Processes, Complex Systems, and Applications of the Diffusion Equation. Dr. Lenzi is on the Editorial Board of Journal of Geophysics and Engineering, Mathematical Problems in Engineering, and Quantum Reports.
Affiliations and expertise
Associate Professor of Physics, Universidade Estaudal de Ponta Grossa, BrazilRead Recent Trends in Fractional Calculus and Its Applications on ScienceDirect