| Description |
1 online resource (268 p.) |
| Contents |
Cover -- Title Page -- Copyright Page -- Contents -- Preface -- Acknowledgments -- About the Authors -- Chapter 1 Introduction to Fractional Calculus -- 1.1 Introduction -- 1.2 Birth of Fractional Calculus -- 1.3 Useful Mathematical Functions -- 1.3.1 The Gamma Function -- 1.3.2 The Beta Function -- 1.3.3 The Mittag-Leffler Function -- 1.3.4 The Mellin-Ross Function -- 1.3.5 The Wright Function -- 1.3.6 The Error Function -- 1.3.7 The Hypergeometric Function -- 1.3.8 The H-Function -- 1.4 Riemann-Liouville (R-L) Fractional Integral and Derivative -- 1.5 Caputo Fractional Derivative |
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1.6 Grünwald-Letnikov Fractional Derivative and Integral -- 1.7 Riesz Fractional Derivative and Integral -- 1.8 Modified Riemann-Liouville Derivative -- 1.9 Local Fractional Derivative -- 1.9.1 Local Fractional Continuity of a Function -- 1.9.2 Local Fractional Derivative -- References -- Chapter 2 Recent Trends in Fractional Dynamical Models and Mathematical Methods -- 2.1 Introduction -- 2.2 Fractional Calculus: A Generalization of Integer-Order Calculus -- 2.3 Fractional Derivatives of Some Functions and Their Graphical Illustrations -- 2.4 Applications of Fractional Calculus |
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2.4.1 N.H. Abel and Tautochronous problem -- 2.4.2 Ultrasonic Wave Propagation in Human Cancellous Bone -- 2.4.3 Modeling of Speech Signals Using Fractional Calculus -- 2.4.4 Modeling the Cardiac Tissue Electrode Interface Using Fractional Calculus -- 2.4.5 Application of Fractional Calculus to the Sound Waves Propagation in Rigid Porous Materials -- 2.4.6 Fractional Calculus for Lateral and Longitudinal Control of Autonomous Vehicles -- 2.4.7 Application of Fractional Calculus in the Theory of Viscoelasticity -- 2.4.8 Fractional Differentiation for Edge Detection |
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2.4.9 Wave Propagation in Viscoelastic Horns Using a Fractional Calculus Rheology Model -- 2.4.10 Application of Fractional Calculus to Fluid Mechanics -- 2.4.11 Radioactivity, Exponential Decay, and Population Growth -- 2.4.12 The Harmonic Oscillator -- 2.5 Overview of Some Analytical/Numerical Methods -- 2.5.1 Fractional Adams-Bashforth/Moulton Methods -- 2.5.2 Fractional Euler Method -- 2.5.3 Finite Difference Method -- 2.5.4 Finite Element Method -- 2.5.5 Finite Volume Method -- 2.5.6 Meshless Method -- 2.5.7 Reproducing Kernel Hilbert Space Method -- 2.5.8 Wavelet Method |
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2.5.9 The Sine-Gordon Expansion Method -- 2.5.10 The Jacobi Elliptic Equation Method -- 2.5.11 The Generalized Kudryashov Method -- References -- Chapter 3 Adomian Decomposition Method -- 3.1 Introduction -- 3.2 Basic Idea of ADM -- 3.3 Numerical Examples -- References -- Chapter 4 Adomian Decomposition Transform Method -- 4.1 Introduction -- 4.2 Transform Methods for the Caputo Sense Derivatives -- 4.3 Adomian Decomposition Laplace Transform Method (ADLTM) -- 4.4 Adomian Decomposition Sumudu Transform Method (ADSTM) -- 4.5 Adomian Decomposition Elzaki Transform Method (ADETM) |
| Notes |
Description based upon print version of record |
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4.6 Adomian Decomposition Aboodh Transform Method (ADATM) |
| Form |
Electronic book
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| Author |
Jena, Subrat K
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Chakraverty, Snehashish
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| ISBN |
9781119696834 |
|
1119696836 |
|
1119697069 |
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9781119697060 |
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