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Title: Fractional Calculus of P-transforms
Authors: Kumar, Dilip
Kilbas, Anatoly
Keywords: P-Transform
Mellin Transform
Laplace Transform
Fractional Integrals and Derivatives
Generalized Hypergeometric Series
Thermonuclear Function
Reaction Rate Probability Integral
Pathway Model
Issue Date: 2010
Publisher: Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Citation: Fractional Calculus and Applied Analysis, Vol. 13, No 3, (2010), 309p-328p
Abstract: The fractional calculus of the P-transform or pathway transform which is a generalization of many well known integral transforms is studied. The Mellin and Laplace transforms of a P-transform are obtained. The composition formulae for the various fractional operators such as Saigo operator, Kober operator and Riemann-Liouville fractional integral and differential operators with P-transform are proved. Application of the P-transform in reaction rate theory in astrophysics in connection with extended nonresonant thermonuclear reaction rate probability integral in the Maxwell-Boltzmann case and cut-off case is established. The behaviour of the kernel functions of type-1 and type-2 P-transform are also studied.
Description: MSC 2010: 44A20, 33C60, 44A10, 26A33, 33C20, 85A99
ISSN: 1311-0454
Appears in Collections:2010

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