978-81-8487-333-7 Publication Year: 2014
Pages: 232 Binding: Hard Back
About the book
FRACTIONAL CALCULUS: Theory and Applications deals with differentiation and integration of arbitrary order. The origin of this subject can be traced back to the end of seventeenth century, the time when Newton and Leibniz developed foundations of differential and integral calculus. Nonetheless, utility and applicability of FC to various branches of science and engineering have been realized only in last few decades. Recent years have witnessed tremendous upsurge in research activities related to the applications of FC in modeling of real-world systems. Unlike the derivatives of integral order, the non-local nature of fractional derivatives correctly models many natural phenomena containing long memory and give more accurate description than their integer counterparts.
The present book comprises of contributions from academicians and leading researchers and gives a panoramic overview of various aspects of this subject:
• Introduction to Fractional Calculus
• Fractional Differential Equations
• Fractional Ordered Dynamical Systems
• Fractional Operators on Fractals
• Local Fractional Derivatives
• Fractional Control Systems
• Fractional Operators and Statistical Distributions
• Applications to Engineering
An Introduction to Fractional Calculus / Solving Nonlinear Fractional Differential Equations / Existence and Uniqueness Theorems: A New Approach / Chaos in Fractional Order Systems / Stability Analysis of Fractional Differential System with Delay / Controllability of Fractional Dynamical Systems / Matrix Variate Fractional Operators and Statistical Distributions / Local Fractional Calculus: A Review / Outline of Calculus on Fractals and Applications / Random Walk and Broad Distributions on Fractal Curves / Some Recent Results on Fractional Diffusions / Introduction to Linear Fractional-order Systems / Fractional-order Nordheim-Fuchs Model for Nuclear Reactor.
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