Presents technologies and practices used in fractional calculus, providing detailed insight into recent developments in and latest research in the field of science, engineering, etc., using fractional calculus.
Fractional calculus is one of the most important divisions of theoretical and applied mathematics. This new book presents a wide variety of interesting technologies and practices used in fractional calculus, providing detailed insight into recent developments and the latest research in the field of science, engineering, etc., using fractional calculus.
The result of the teaching experiences of the editors and authors to engineering and science students, the volume discusses fractional calculus via generalized functions and integral transforms of pathway type; Laplace transformation of fractional integrals and derivatives; estimating the order of derivation in a fractional differential equation; a new class of integro-differential equations with non-singular differential operators; various uses of the Caputo approach; a gingerbread-man discrete system; etc. The various applications of fractional calculus are shown with examples such as for creating and/or solving epidemic models, alcoholism models, model for divorce dynamics, and more.
Giving a rigorous and thorough analysis of various aspects of fractional calculus, this volume helps scientific readers as well as researchers working in the area of fractional calculus to establish the key steps followed in the research methodology and concept development.
1. An Outlook on Fractional Calculus via Generalized Functions and
Integral Transforms of Pathway Type
2. Laplace Transformation of Fractional
Integrals and Derivatives
3. Estimating the Order of Derivation in a
Fractional Differential Equation
4. New Class of Integro-Differential
Equations with Non-Singular Differential Operators
5. Exact Solution of
Fractional Equations
6. Numerical Computation of Fractional Derivatives of
Caputo Type
7. Some Remarks on Caputo-Weighted Integrals and Applications
8.
Periodicity Solutions of K-Symbol Fractional Differential Equations with
Applications
9. Gingerbread-Man Discrete System Formulated by the K-Symbol
Fractional Calculus
10. An Improved Numerical Algorithm for Solving
Multi-Order Fractional Differential Equations
11. Existence Results for
Implicit FFDEs with Tempered Xi-HFD
12. Computational Study of the Fractional
Order of an Alcoholism Model
13. A Statistical-Oriented Application of the
Erdélyi-Kober Fractional Integral in Epidemic Model Problems
14. A
Comprehensive Qualitative Examination of a Fractional-Order Model for Divorce
Dynamics
15. A Numerical Study of the Jaulent-Miodek Model Using Homotopy
Perturbation Transform Technique via the Caputo-Fabrizio Operator
16.
Fractional Kinetic Equation with Incomplete Wright Function
Dharmendra Kumar Singh, PhD, is an Assistant Professor of Mathematics in the School of Basic Sciences at the University Institute of Engineering & Technology (UIET), Chhatrapati Sahau Ji Maharaja University, Kanpur, India. With over 12 years of research and teaching experience in the field of fractional calculus, he focuses his research on special functions, fractional calculus, partial fractional differential equations, and distribution theory. Dr. Singh has published research papers and book chapters on fractional calculus and received a best publication award from The Society for Special Functions and Their Applications. He is a reviewer for many reputed international journals.
Mehmet Yavuz, PhD, is an Associate Professor in the Mathematics and Computer Sciences Department, Necmettin Erbakan University, Türkiye. He has published more than 85 research papers in reputed journals, 60 conference papers, book chapters, and the book Fractional Calculus: New Applications in Understanding Nonlinear Phenomena. He has received awards for his work. His research interests lie in biomathematics, infectious disease dynamics, population dynamics, stochastic analysis, calcium dynamics, fractional mathematical models, fractional mathematical theory and methods, bifurcation analysis, and dynamical control theory. Apart from being an associate editor for several esteemed journals, he is the Editor-in-Chief of the journal Mathematical Modelling and Numerical Simulation with Applications and the Bulletin of Biomathematics.v
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