P-Transform Mellin Transform H-Function 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.
