Fractional Calculus of P-transforms

Kumar, Dilip, and Kilbas, Anatoly. "Fractional Calculus of P-transforms." Fractional Calculus and Applied Analysis 13.3 (2010): 309-328. <http://eudml.org/doc/219583>.

@article{Kumar2010,
abstract = {MSC 2010: 44A20, 33C60, 44A10, 26A33, 33C20, 85A99The 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.},
author = {Kumar, Dilip, Kilbas, Anatoly},
journal = {Fractional Calculus and Applied Analysis},
keywords = {P-Transform; Mellin Transform; H-Function; Laplace Transform; Fractional Integrals and Derivatives; Generalized Hypergeometric Series; Thermonuclear Function; Reaction Rate Probability Integral; Pathway Model; -transform; Mellin and Laplace transform; fractional calculus; generalized hypergeometric series; probability integral},
language = {eng},
number = {3},
pages = {309-328},
publisher = {Institute of Mathematics and Informatics Bulgarian Academy of Sciences},
title = {Fractional Calculus of P-transforms},
url = {http://eudml.org/doc/219583},
volume = {13},
year = {2010},
}

TY - JOUR
AU - Kumar, Dilip
AU - Kilbas, Anatoly
TI - Fractional Calculus of P-transforms
JO - Fractional Calculus and Applied Analysis
PY - 2010
PB - Institute of Mathematics and Informatics Bulgarian Academy of Sciences
VL - 13
IS - 3
SP - 309
EP - 328
AB - MSC 2010: 44A20, 33C60, 44A10, 26A33, 33C20, 85A99The 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.
LA - eng
KW - P-Transform; Mellin Transform; H-Function; Laplace Transform; Fractional Integrals and Derivatives; Generalized Hypergeometric Series; Thermonuclear Function; Reaction Rate Probability Integral; Pathway Model; -transform; Mellin and Laplace transform; fractional calculus; generalized hypergeometric series; probability integral
UR - http://eudml.org/doc/219583
ER -