P-Transform Mellin Transform H-Function Laplace Transform Fractional Integrals and Derivatives Generalized Hypergeometric Series Thermonuclear Function Reaction Rate Probability Integral Pathway Model
Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Fractional Calculus and Applied Analysis, Vol. 13, No 3, (2010), 309p-328p
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.