Please use this identifier to cite or link to this item: http://hdl.handle.net/10525/1655

 Title: Fractional Calculus of P-transforms Authors: Kumar, DilipKilbas, Anatoly Keywords: P-TransformMellin TransformH-FunctionLaplace TransformFractional Integrals and DerivativesGeneralized Hypergeometric SeriesThermonuclear FunctionReaction Rate Probability IntegralPathway 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 URI: http://hdl.handle.net/10525/1655 ISSN: 1311-0454 Appears in Collections: 2010

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