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Generalized Functions for the Fractional Calculus
AUTHOR | Nasa, National Aeronautics and Space Adm |
PUBLISHER | Independently Published (09/25/2018) |
PRODUCT TYPE | Paperback (Paperback) |
Description
Previous papers have used two important functions for the solution of fractional order differential equations, the Mittag-Leffler functionE(sub q) at(exp q)](1903a, 1903b, 1905), and the F-function F(sub q) a, t] of Hartley & Lorenzo (1998). These functions provided direct solution and important understanding for the fundamental linear fractional order differential equation and for the related initial value problem (Hartley and Lorenzo, 1999). This paper examines related functions and their Laplace transforms. Presented for consideration are two generalized functions, the R-function and the G-function, useful in analysis and as a basis for computation in the fractional calculus. The R-function is unique in that it contains all of the derivatives and integrals of the F-function. The R-function also returns itself on qth order differ-integration. An example application of the R-function is provided. A further generalization of the R-function, called the G-function brings in the effects of repeated and partially repeated fractional poles. Lorenzo, Carl F. and Hartley, Tom T. Glenn Research Center NASA/TP-1999-209424, NAS 1.60:209424, E-11944
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Product Details
ISBN-13:
9781724034335
ISBN-10:
1724034332
Binding:
Paperback or Softback (Trade Paperback (Us))
Content Language:
English
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Page Count:
38
Carton Quantity:
108
Product Dimensions:
8.50 x 0.08 x 11.00 inches
Weight:
0.25 pound(s)
Country of Origin:
US
Subject Information
BISAC Categories
Science | Space Science - General
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Previous papers have used two important functions for the solution of fractional order differential equations, the Mittag-Leffler functionE(sub q) at(exp q)](1903a, 1903b, 1905), and the F-function F(sub q) a, t] of Hartley & Lorenzo (1998). These functions provided direct solution and important understanding for the fundamental linear fractional order differential equation and for the related initial value problem (Hartley and Lorenzo, 1999). This paper examines related functions and their Laplace transforms. Presented for consideration are two generalized functions, the R-function and the G-function, useful in analysis and as a basis for computation in the fractional calculus. The R-function is unique in that it contains all of the derivatives and integrals of the F-function. The R-function also returns itself on qth order differ-integration. An example application of the R-function is provided. A further generalization of the R-function, called the G-function brings in the effects of repeated and partially repeated fractional poles. Lorenzo, Carl F. and Hartley, Tom T. Glenn Research Center NASA/TP-1999-209424, NAS 1.60:209424, E-11944
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