On the Solution of Kinetic Equation for Katugampola Type Fractional Differential Equations

Ahmed, Wagdi F. S.; PAWAR, D.D.; Salamooni, Ahmad Y. A.

doi:10.1080/1726037X.2021.1966946

Open Access Research Article

On the Solution of Kinetic Equation for Katugampola Type Fractional Differential Equations

^*Wagdi F. S. AhmedCorresponding authorwagdialakel@gmail.comSchool of Mathematical SciencesSwami Raman and Teerth Marathwada UniversityNanded, Maharashtra, 431606, India0000-0002-5115-4355View full profile → , D.D. PAWARdypawar@yahoo.comSchool of Mathematical SciencesSwami Raman and Teerth Marathwada UniversityNanded, Maharashtra, 431606, India0000-0001-8986-5243View full profile → , Ahmad Y. A. Salamooniayousss83@gmail.comSchool of Mathematical SciencesSwami Raman and Teerth Marathwada UniversityNanded, Maharashtra, 431606, IndiaView full profile →

* Corresponding author · click or hover a name for details

pp. 125–134Vol. 19Issue 1January 2021DOI: 10.1080/1726037X.2021.1966946XML

Received:: 05 Jun 2020
Accepted:: 21 Dec 2020
Published Online:: 29 Sep 2021
Article type:: Research Article
Language:: EN
Article no.:: 1726037X.2021.1966946
Pages:: 125–134

Abstract

In this article, we have investigate a solution of fractional Kinetic equation involving Katugampola type fractional integral by using H – function. We also present the solution of Kinetic equation involving Katugampola type fractional integral with the help of generalized I – function and Mellin transform.

Keywords

Fractional Kinetic equation Katugampola type fractional integralMittag-Leffler functionMellin transform

Subject Classifications

74A2533C2026A3344A1533E12

References

AhmedW.F.S and PawarD.D., Application of Sumudu Transform on Fractional Kinetic Equation Pertainingto the Generalized k-Wright Function, Adv.Math , Sci. J ( 9 ) ( 2020 ), no. 10 , 8091 – 8103
Al-SaqabiB. N., TuanV. K., Solution of a fractional differintegral equation , Integral Transf. Spec. Funct . 4 ( 4 ) ( 1996 ) 321 - 326 . doi: 10.1080/10652469608819118
HauboldH. J., MathaiA. M., The fractional kinetic equation and thermonuclear functions , Astrophys. Space Sci . 273 ( 2000 ) 53 - 63 . doi: 10.1023/A:1002695807970
KatugampolaU. N., Existence and uniqueness results for a class of generalized fractional differential equations, arXiv:1411.5229v2[math.CA] 9 Jun 2016.
KatugampolaU. N., Mellin Transforms of Generalized Fractional Integrals and Derivatives , Applied Mathematics and Computation 00 ( 2018 ) 1 - 17 .
KilbasA. A., SrivastavaH. M. and TrujilloJ. J., Theory and Applications of Fractional Differential Equations , Elsevier , Amsterdam ( 2006 ).
KiryakovaV., Generalized Fractional Calculus and Applications , John Wiley , New York, 1994 .
Mittag-LefflerG. M., Sur la nouvelle fonction ( ) , C.R. Acad. Sci. Paris 137 ( 1903 ) 554 - 558 .
NisarK. S, AbouzaidM. S and BelgacemF. B. M, Certain Image Formulae and Fractional Kinetic Equations of Generalized k-Bessel Functions via the Sumudu Transform , Int. J.Appl.Comput. Math ( 2020 )
SahaU. K., AroraL. K. and DuttaB. K., Integrals Involving – Function , Gen. Math. Notes , Vol. 6 , No. 1 , Sep. 2011 , pp. 1 - 14 .
SaichevA., ZaslavskyM., Fractional kinetic equations: solutions and applications , Chaos 7 ( 4 ) ( 1997 ) 753 - 764 . doi: 10.1063/1.166272
SalamooniA. Y. A., PawarD. D., Katugampola Fractional Calculus With Generalized k – Wright Function, arXiv:1909.07880v1[math.AP] 11 Sep 2019.
SaxenaR. K., MathaiA. M., HauboldH. J., On fractional kinetic equations , Astrophys. Space Sci . 282 ( 2002 ) 281 - 287 . doi: 10.1023/A:1021175108964
SaxenaR. K., MathaiA. M., HauboldH. J., On generalized fractional kinetic equations , Physica A 344 ( 2004 ) 653 - 664 .
SaxenaR. K., MathaiA. M., HauboldH. J., Fractional reaction-diffusion equations , Astrophys. Space Sci. 305 ( 3 ) ( 2006 ) 289 - 296 . doi: 10.1007/s10509-006-9189-6
SaxenaR. K., MathaiA. M., HauboldH. J., Unified fractional kinetic equation and a fractional diffusion equation , Astrophys. Space Sci . 290 ( 3/4 ) ( 2004 ) 299 - 310 . doi: 10.1023/B:ASTR.0000032531.46639.a7
SaxenaR. K., MathaiA. M., HauboldH. J., Solution of generalized fractional-diffusion equations , Astrophys. Space Sci . 305 ( 3 ) ( 2006 ) 305313 .
SaxenaR. K., MathaiA. M., HauboldH. J., The H – Function Theoand Applications, ©Springer Science+Business Media, LLC 2010.
SaxenaR. K., KallaS. L., On the solutions of certain fractional kinetic equations , Applied Mathematics and Computation 199 ( 2008 ) 504 - 511 . doi: 10.1016/j.amc.2007.10.005
SutharD. L., PurohitS. D, and AraciS, Solution of Fractional Kinetic Equations Associated with the (p, q)-Mathieu-Type Series, Hindawi Discrete Dyn. Nat. Soc. Volume 2020, Article ID 8645161

Views: 53Downloads: 89Citations: 3

[1] AhmedW.F.S and PawarD.D., Application of Sumudu Transform on Fractional Kinetic Equation Pertainingto the Generalized k-Wright Function, Adv.Math , Sci. J ( 9 ) ( 2020 ), no. 10 , 8091 – 8103

[2] Al-SaqabiB. N., TuanV. K., Solution of a fractional differintegral equation , Integral Transf. Spec. Funct . 4 ( 4 ) ( 1996 ) 321 - 326 . doi: 10.1080/10652469608819118

[3] HauboldH. J., MathaiA. M., The fractional kinetic equation and thermonuclear functions , Astrophys. Space Sci . 273 ( 2000 ) 53 - 63 . doi: 10.1023/A:1002695807970

[4] KatugampolaU. N., Existence and uniqueness results for a class of generalized fractional differential equations, arXiv:1411.5229v2[math.CA] 9 Jun 2016.

[5] KatugampolaU. N., Mellin Transforms of Generalized Fractional Integrals and Derivatives , Applied Mathematics and Computation 00 ( 2018 ) 1 - 17 .

[6] KilbasA. A., SrivastavaH. M. and TrujilloJ. J., Theory and Applications of Fractional Differential Equations , Elsevier , Amsterdam ( 2006 ).

[7] KiryakovaV., Generalized Fractional Calculus and Applications , John Wiley , New York, 1994 .

[8] Mittag-LefflerG. M., Sur la nouvelle fonction ( ) , C.R. Acad. Sci. Paris 137 ( 1903 ) 554 - 558 .

[9] NisarK. S, AbouzaidM. S and BelgacemF. B. M, Certain Image Formulae and Fractional Kinetic Equations of Generalized k-Bessel Functions via the Sumudu Transform , Int. J.Appl.Comput. Math ( 2020 )

[10] SahaU. K., AroraL. K. and DuttaB. K., Integrals Involving – Function , Gen. Math. Notes , Vol. 6 , No. 1 , Sep. 2011 , pp. 1 - 14 .

[11] SaichevA., ZaslavskyM., Fractional kinetic equations: solutions and applications , Chaos 7 ( 4 ) ( 1997 ) 753 - 764 . doi: 10.1063/1.166272

[12] SalamooniA. Y. A., PawarD. D., Katugampola Fractional Calculus With Generalized k – Wright Function, arXiv:1909.07880v1[math.AP] 11 Sep 2019.

[13] SaxenaR. K., MathaiA. M., HauboldH. J., On fractional kinetic equations , Astrophys. Space Sci . 282 ( 2002 ) 281 - 287 . doi: 10.1023/A:1021175108964

[14] SaxenaR. K., MathaiA. M., HauboldH. J., On generalized fractional kinetic equations , Physica A 344 ( 2004 ) 653 - 664 .

[15] SaxenaR. K., MathaiA. M., HauboldH. J., Fractional reaction-diffusion equations , Astrophys. Space Sci. 305 ( 3 ) ( 2006 ) 289 - 296 . doi: 10.1007/s10509-006-9189-6

[16] SaxenaR. K., MathaiA. M., HauboldH. J., Unified fractional kinetic equation and a fractional diffusion equation , Astrophys. Space Sci . 290 ( 3/4 ) ( 2004 ) 299 - 310 . doi: 10.1023/B:ASTR.0000032531.46639.a7

[17] SaxenaR. K., MathaiA. M., HauboldH. J., Solution of generalized fractional-diffusion equations , Astrophys. Space Sci . 305 ( 3 ) ( 2006 ) 305313 .

[18] SaxenaR. K., MathaiA. M., HauboldH. J., The H – Function Theoand Applications, ©Springer Science+Business Media, LLC 2010.

[19] SaxenaR. K., KallaS. L., On the solutions of certain fractional kinetic equations , Applied Mathematics and Computation 199 ( 2008 ) 504 - 511 . doi: 10.1016/j.amc.2007.10.005

[20] SutharD. L., PurohitS. D, and AraciS, Solution of Fractional Kinetic Equations Associated with the (p, q)-Mathieu-Type Series, Hindawi Discrete Dyn. Nat. Soc. Volume 2020, Article ID 8645161

Journal of Dynamical Systems and Geometric Theories

WoS JIF 2026 : 0.5 (Q3)

On the Solution of Kinetic Equation for Katugampola Type Fractional Differential Equations

Abstract

Keywords

Subject Classifications

References