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Hardcover Artificial Neural Networks: Methods and Applications in Fractional Order Systems Book

ISBN: 9811218803

ISBN13: 9789811218804

Artificial Neural Networks: Methods and Applications in Fractional Order Systems

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Book Overview

This is the first book that uses Artificial Neural Networks (ANN) to solve fractional order systems. As a powerful data modeling tool, information is processed through neurons in parallel manner to solve a specific problem. Knowledge is acquired through learning and stored with inter neuron connections strength which are expressed by numerical values called weights. These weights are used to complete output signal values for new testing input signal value.In this book, multi-layer ANN model will be used to handle fractional order differential equations (FDEs). The network is trained using a back-propagation unsupervised learning algorithm which is based on the gradient descent rule. The ANN approximate solution of FDEs may be expressed as a sum of two terms; the first part satisfies boundary or initial conditions, and the second term contains ANN output with network parameters (weights and biases).Next, single layer Functional Link Artificial Neural Network (FLANN) models will be included for solving the FDEs. In FLANN the hidden layer is replaced by a functional expansion block for enhancement of the input patterns using orthogonal polynomials such as Chebyshev, Legendre, Hermite, etc. The computations become efficient because the procedure does not need to have hidden layer. Thus, the numbers of network parameters are less than the traditional ANN model.Varieties of FDEs will be addressed to show the reliability and efffectiveness of ANN. Singular nonlinear fractional Lane-Emden type equations, fractional vibration problems viz. Bagley-Torvik equations, fractional electrical problems viz. RLC, RC, LC circuit problems, Duffing oscillator problems with fractional derivatives etc. will be handled using multi-layer ANN and single layer FLANN models.
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Customer Reviews

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Rated 5 stars
Truly a gem of a book.

This elegant little book covers the elements of a senior or 1st year graduate course on complex analysis, although a really good mathematics program like at Berkeley may look upon it as providing some material for a junior course in advanced calculus. It is not a new book, i.e. it predates the space age and computers, but the material is timeless and fundamental. Highly recommended for those who want some exposure to a first-class...

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Rated 4 stars
a short review of the book theory of functions by Knopp

Despite not being a very recent book, a graduate student of mathematics who has to prepare complex analysis as a general topic for his qualifying examinations may find that this text covers all the essential material in the subject.

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