Numerical Methods for Fractional Differentiation. (2019)

• Record Type: Book
• Further Information: Note: Kolade M. Owoladi, Abdon Atangana.
• Other Names: Owolabi, Kolade M; Atangana, Abdon
• Contents: Intro; Preface; Acknowledgements; Contents; About the Authors; 1 Review of Fractional Differentiation; 1.1 Special Functions; 1.1.1 The Gamma Function; 1.1.2 The Beta Function; 1.1.3 The Complementary Error Function; 1.1.4 The Mittag-Leffler Function; 1.1.5 Laplace Transformation and Convolution; 1.2 Riemann-Liouville Fractional Differentiation; 1.3 Caputo Fractional Derivative; 1.4 Classical Fractional Derivatives; 1.5 Partial Riemann-Liouville Fractional Derivative; 1.6 Fractional Operators with Variable Order; 1.7 Tempered Fractional Differentiation 1.7.1 Properties of Tempered Fractional Derivative and Integral1.7.2 Laplace Transforms of the Tempered Fractional Calculus; 1.8 Caputo-Fabrizio Fractional Differentiation; 1.8.1 Caputo-Fabrizio Fractional Derivative in Caputo Sense; 1.8.2 The Laplace Transform of the Caputo-Fabrizio Fractional Derivative; 1.8.3 Fourier Transform of Fractional Gradient, Divergence and Laplacian; 1.8.4 Caputo-Fabrizio Fractional Derivative in Riemann-Liouville Sense; 1.9 Stretch Fractional Differentiation; 1.10 The Atangana-Baleanu Fractional Derivative and Integral 1.11 The Riesz Potential and Riesz Fractional Derivatives1.11.1 The Atangana-Gómez Fractional Derivative; References; 2 Finite Difference Approximations; 2.1 Finite Difference Approximation Schemes; 2.1.1 Taylor Series and Finite Difference Approximation; 2.1.2 Higher Order Finite Difference Approximation; 2.2 Error Analysis; 2.2.1 Illustrative Example; 2.2.2 Order of Accuracy and Consistency; 2.2.3 Matrix Notation; 2.3 Numerical Stability and Convergence Analysis; 2.3.1 Von Neumann (Fourier Series) Stability Analysis; 2.3.2 Matrix Stability Analysis; 2.3.3 Convergence; 2.3.4 Symmetry 2.4 Numerical Results2.5 Finite Difference Approximations Schemes for Fractional Equations; 2.5.1 Matrix Representation of the Finite Difference Schemes; 2.5.2 Convergence Analysis of Fractional Finite Difference Schemes; 2.5.3 Stability Analysis of Fractional Finite Difference Schemes; 2.6 Numerical Approximation of Time-Fractional Sub-diffusion Process with the Second-Order Implicit Difference Method; 2.6.1 Second-Order Implicit Difference Approximation; References; 3 Numerical Approximation of Riemann-Liouville Differentiation; 3.1 Numerical Approximation for Time Derivative 3.2 Numerical Approximation for Space First-Order Derivative3.3 Numerical Approximation for Space Second-Order Derivative; 3.4 Crank-Nicholson Scheme for Time-Fractional Differential Equations in Riemann-Liouville Sense; 3.5 A New Definition of Fractional Time Derivative in Riemann-Liouville Sense; References; 4 Numerical Approximation of Caputo Differentiation; 4.1 Numerical Approximation for Time Derivative; 4.2 Numerical Approximation for Space First-Order Derivative; 4.3 Numerical Methods for Fractional Evolution Equations; 4.3.1 Fractional Euler and Adams Methods
• Publisher Details: Singapore : Springer
• Publication Date: 2019
• Extent: 1 online resource (338 pages)
• Subjects: 515/.35; Fractional differential equations; Fractional differential equations; Electronic books
• Languages: English
• ISBNs: 9789811500985; 9811500983
• Related ISBNs: 9789811500978
• Notes: Note: Includes bibliographical references.; Note: Print version record.
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.