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Fractional dynamic calculus and frac...

Georgiev, Svetlin G.

Fractional dynamic calculus and fractional dynamic equations on time scales

Record Type:	Electronic resources : Monograph/item
Title/Author:	Fractional dynamic calculus and fractional dynamic equations on time scalesby Svetlin G. Georgiev.
Author:	Georgiev, Svetlin G.
Published:	Cham :Springer International Publishing :2018.
Description:	viii, 360 p. :ill., digital ;24 cm.
Contained By:	Springer eBooks
Subject:	Fractional calculus.
Online resource:	http://dx.doi.org/10.1007/978-3-319-73954-0
ISBN:	9783319739540$q(electronic bk.)

Fractional dynamic calculus and fractional dynamic equations on time scales
Georgiev, Svetlin G.

Fractional dynamic calculus and fractional dynamic equations on time scales[electronic resource] /by Svetlin G. Georgiev. - Cham :Springer International Publishing :2018. - viii, 360 p. :ill., digital ;24 cm.

1. Elements of the Time Scale Calculus -- 2. The Laplace Transform on Time Scales -- 3. The Convolution on Time Scales -- 4. The Riemann-Liouville Fractional D-Integral and the Riemann-Liouville Fractional D-Derivative on Time Scales -- 5. Cauchy Type Problem with the Riemann-Liouville Fractional D-Derivative -- 6. Riemann-Liouville Fractional Dynamic Equations with Constant Coefficients -- 7. The Caputo Fractional D-Derivative on Time Scales -- 8. Cauchy Type Problem with the Caputo Fractional D-Derivative -- 9. Caputo Fractional Dynamic Equations with Constant Coefficients -- Appendix: The Gamma Function -- Appendix: The Gamma Function -- Index.

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.

ISBN: 9783319739540$q(electronic bk.)

Standard No.: 10.1007/978-3-319-73954-0doiSubjects--Topical Terms:

208302
Fractional calculus.

LC Class. No.: QA314 / .G467 2018

Dewey Class. No.: 515.83

Fractional dynamic calculus and fractional dynamic equations on time scales
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505 0 $a 1. Elements of the Time Scale Calculus -- 2. The Laplace Transform on Time Scales -- 3. The Convolution on Time Scales -- 4. The Riemann-Liouville Fractional D-Integral and the Riemann-Liouville Fractional D-Derivative on Time Scales -- 5. Cauchy Type Problem with the Riemann-Liouville Fractional D-Derivative -- 6. Riemann-Liouville Fractional Dynamic Equations with Constant Coefficients -- 7. The Caputo Fractional D-Derivative on Time Scales -- 8. Cauchy Type Problem with the Caputo Fractional D-Derivative -- 9. Caputo Fractional Dynamic Equations with Constant Coefficients -- Appendix: The Gamma Function -- Appendix: The Gamma Function -- Index.
520 $a 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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