| Document Type
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BL
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| Record Number
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864568
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| Main Entry
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Georgiev, Svetlin
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| Title & Author
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Fractional dynamic calculus and fractional dynamic equations on time scales /\ Svetlin G. Georgiev.
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| Publication Statement
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Cham, Switzerland :: Springer,, [2018]
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, ©2018
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| Page. NO
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1 online resource
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| ISBN
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3319739549
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: 9783319739540
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3319739530
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9783319739533
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| Bibliographies/Indexes
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Includes bibliographical references.
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| Contents
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Intro; Preface; Contents; 1 Elements of Time Scale Calculus; 1.1 Forward and Backward Jump Operators, Graininess Function; 1.2 Differentiation; 1.3 Mean Value Theorems; 1.4 Integration; 1.5 The Exponential Function; 1.5.1 Hilger's Complex Plane; 1.5.2 Definition and Properties of the Exponential Function; 1.5.3 Examples for Exponential Functions; 1.6 Hyperbolic and Trigonometric Functions; 1.7 Dynamic Equations; 1.8 Power Series on Time Scales; 1.9 Advanced Practical Problems; 2 The Laplace Transform on Time Scales; 2.1 Definition and Properties.
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9.2 Inhomogeneous Caputo Fractional Dynamic Equations with Constant Coefficients9.3 Advanced Practical Problems; 10 Appendix: The Gamma Function; 10.1 Definition of the Gamma Function; 10.2 Some Properties of the Gamma Function; 10.3 Limit Representation of the Gamma Function; 11 Appendix: The Beta Function; 11.1 Definition of the Beta Function; 11.2 Properties of the Beta Function; 11.3 An Application; References; Index.
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| Abstract
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Pedagogically organized, this monograph introduces fractional calculus and fractional dynamic equations on time scales in relation to mathematical physics applications and problems. Beginning with the definitions of forward and backward jump operators, the book builds from Stefan Hilger's basic theories on time scales and examines recent developments within the field of fractional calculus and fractional equations. Useful tools are provided for solving differential and integral equations as well as various problems involving special functions of mathematical physics and their extensions and generalizations in one and more variables. Much discussion is devoted to Riemann-Liouville fractional dynamic equations and Caputo fractional dynamic equations. Intended for use in the field and designed for students without an extensive mathematical background, this book is suitable for graduate courses and researchers looking for an introduction to fractional dynamic calculus and equations on time scales.
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| Subject
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Differential equations.
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| Subject
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Dynamics-- Mathematics.
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| Subject
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Fractional calculus.
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Calculus.
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Differential equations.
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| Subject
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Dynamics-- Mathematics.
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| Subject
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Fractional calculus.
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| Subject
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Integral calculus equations.
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| Subject
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Mathematical physics.
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| Subject
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MATHEMATICS-- Calculus.
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MATHEMATICS-- Mathematical Analysis.
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| Subject
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Mathematics
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Calculus
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Integral Transforms, Operational Calculus
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Mathematical Physics
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| Subject
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Measure and Integration
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| Dewey Classification
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515.83
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| LC Classification
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QA314
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