Geodesic
Fractional Calculus of P-transforms
Fractional calculus and applied analysis, Tome 13 (2010) no. 3, pp. 309-328.

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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.
Keywords: P-Transform, Mellin Transform, H-Function, Laplace Transform, Fractional Integrals and Derivatives, Generalized Hypergeometric Series, Thermonuclear Function, Reaction Rate Probability Integral, Pathway Model 
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     title = {Fractional {Calculus} of {P-transforms}},
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     url = {http://geodesic.mathdoc.fr/item/FCAA_2010_13_3_a5/}
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Kumar, Dilip; Kilbas, Anatoly. Fractional Calculus of P-transforms. Fractional calculus and applied analysis, Tome 13 (2010) no. 3, pp. 309-328. http://geodesic.mathdoc.fr/item/FCAA_2010_13_3_a5/