Umfang:
1 Online-Ressource (379 Seiten)
ISBN:
9783110472097
Inhalt:
The book is devoted to recent developments in the theory of fractional calculus and its applications. Particular attention is paid to the applicability of this currently popular research field in various branches of pure and applied mathematics. In particular, the book focuses on the more recent results in mathematical physics, engineering applications, theoretical and applied physics as quantum mechanics, signal analysis, and in those relevant research fields where nonlinear dynamics occurs and several tools of nonlinear analysis are required. Dynamical processes and dynamical systems of fractional order attract researchers from many areas of sciences and technologies, ranging from mathematics and physics to computer science.
Inhalt:
Intro -- Fractional Dynamics -- Local Fractional Calculus on Shannon Wavelet Basis -- 1 Introduction -- 2 Preliminary Remarks -- 2.1 Shannon Wavelets in the Fourier Domain -- 2.2 Properties of the Shannon Wavelet -- 3 Connection Coefficients -- 3.1 Properties of Connection Coefficients -- 4 Differential Properties of L2( R )-functions in Shannon Wavelet Basis -- 4.1 Taylor Series -- 4.2 Functional Equations -- 4.3 Error of the Approximation by Connection Coefficients -- 5 Fractional Derivatives of the Wavelet Basis -- 5.1 Complex Shannon Wavelets on Fractal Sets of Dimension -- 5.2 Local Fractional Derivatives of Complex Functions -- 5.3 Example: Fractional Derivative of a Gaussian on a Fractal Set -- Discretely and Continuously Distributed Dynamical Systems with Fractional Nonlocality -- 1 Introduction -- 2 Lattice with Long-range Properties -- 3 Lattice Fractional Nonlinear Equations -- 4 Continuum Fractional Derivatives of the Riesz Type -- 5 From Lattice Equations to Continuum Equations -- 6 Fractional Continuum Nonlinear Equations -- 7 Conclusion -- Temporal Patterns in Earthquake Data-series -- 1 Introduction -- 2 Dataset -- 3 Mathematical Tools -- 3.1 Hierarchichal Clustering -- 3.2 Multidimensional Scaling -- 4 Data Analysys and Pattern Visualization -- 4.1 Hierarchical Clustering Analysis and Comparison -- 4.2 MDS Analysis and Visualization -- 5 Conclusions -- An Integral Transform arising from Fractional Calculus -- 1 Integral Transform R -- 2 Dirac's -function and R -- 3 Space of Generalized Functions Spanned by a(n) -- 4 Extended Borel Transform -- 5 The Transform R and Extended Borel Transform -- 6 Application of R to Fractional Differential Equations -- Approximate Solutions to Time-fractional Models by Integral-balance Approach -- 1 Introduction -- 1.1 Subdiffusion -- 1.2 Time-Fractional Derivatives in Rheology.
Anmerkung:
Description based on publisher supplied metadata and other sources
Weitere Ausg.:
ISBN 9783110472080
Weitere Ausg.:
Erscheint auch als Druck-Ausgabe ISBN 9783110472080
Sprache:
Englisch
Fachgebiete:
Mathematik
Schlagwort(e):
Gebrochene Analysis
;
Mathematik
;
Angewandte Mathematik
;
Nichtlineare Dynamik
URL:
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