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The Fundamentals of Fractional Calculus
About this book
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.
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Information
Table of contents
- Cover Page
- Half Title page
- Title Page
- Copyright Page
- About the Editors
- Contents
- Contributors
- Acknowledgment
- Preface
- Chapter 1 An Outlook on Fractional Calculus via Generalized Functions and Integral Transforms of Pathway Type
- Chapter 2 Laplace Transformation of Fractional Integrals and Derivatives
- Chapter 3 Estimating the Order of Derivation in a Fractional Differential Equation
- Chapter 4 New Class of Integro-Differential Equations with Non-Singular Differential Operators
- Chapter 5 Exact Solution of Fractional Equations
- Chapter 6 Numerical Computation of Fractional Derivatives of Caputo Type
- Chapter 7 Some Remarks on Caputo-Weighted Integrals and Applications
- Chapter 8 Periodicity Solutions of k-Symbol Fractional Differential Equations with Applications
- Chapter 9 Gingerbread-man Discrete System Formulated by the k-Symbol Fractional Calculus
- Chapter 10 An Improved Numerical Algorithm for Solving Multi-Order Fractional Differential Equations
- Chapter 11 Existence Results for Implicit FFDEs with Tempered Ξ-HFD
- Chapter 12 Computational Study of the Fractional Order of an Alcoholism Model
- Chapter 13 A Statistical Application of the Erdélyi-Kober Fractional Integral in Epidemic Modeling Problems
- Chapter 14 A Comprehensive Qualitative Examination of a Fractional-Order Model for Divorce Dynamics
- Chapter 15 A Numerical Study of the Jaulent-Miodek Model Using the Homotopy Perturbation Transform Technique with the Caputo-Fabrizio Operator
- Chapter 16 Fractional Kinetic Equation with Incomplete Wright Function
- Index