# Fractional Calculus of P-transforms

Fractional Calculus and Applied Analysis (2010)

- Volume: 13, Issue: 3, page 309-328
- ISSN: 1311-0454

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topKumar, 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 -

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