On the Generalization of Fractional Kinetic Equation Comprising Incomplete H-Function


Download PDF

Authors: K. JANGID, S. D. PUROHIT, R. AGARWAL AND R. P. AGARWAL

DOI: 10.46793/KgJMat2305.701J

Abstract:

In the present work, a novel and even more generalized fractional kinetic equation has been formulated in terms of polynomial weighted incomplete H-function, incomplete Fox-Wright function and incomplete generalized hypergeometric function, considering the importance of the fractional kinetic equations arising in the various science and engineering problems. All the derived findings are of natural type and can produce a variety of fractional kinetic equations and their solutions.



Keywords:

Fractional kinetic equation, fractional calculus, incomplete H-functions, incomplete Fox-Wright functions, incomplete generalized hypergeometric functions.



References:

[1]   H. Habenom, D. L. Suthar, D. Baleanu and S. D. Purohit, A numerical simulation on the effect of vaccination and treatments for the fractional hepatitis B model, Journal of Computational and Nonlinear Dynamics 16(1) (2021), Paper ID 011004. https://doi.org/10.1115/1.4048475

[2]   

Kritika, R. Agarwal and S. D. Purohit, Mathematical model for anomalous subdiffusion using conformable operator, Chaos Solitons & Fractals 140 (2020), Paper ID 110199.https://doi.org/10.1016/j.chaos.2020.110199

[3]   R. Agarwal, M. P. Yadav, D. Baleanu and S. D. Purohit, Existence and uniqueness of miscible flow equation through porous media with a nonsingular fractional derivative, AIMS Mathematics 5(2) (2020), 1062–1073. https://doi.org/10.3934/math.2020074

[4]   R. Agarwal, S. D. Purohit and Kritika, A mathematical fractional model with non-singular kernel for thrombin-receptor activation in calcium signaling, Math. Methods Appl. Sci. 42 (2019), 7160–7171.https://doi.org/10.1002/mma.5822

[5]   M. Chand, J. C. Prajapati and E. Bonyah, Fractional integrals and solution of fractional kinetic equations involving k-Mittag-Leffler function, Trans. A. Razmadze Math. Inst. 171(2) (2017), 144–166. https://doi.org/10.1016/j.trmi.2017.03.003

[6]   R. K. Gupta, A. Atangana, B. S. Shaktawat and S. D. Purohit, On the solution of generalized fractional kinetic equations involving generalized M-series, Caspian Journal of Applied Mathematics, Ecology and Economics 7(1) (2019), 88–98.

[7]   H. Habenom, D. L. Suthar and M. Gebeyehu, Application of Laplace transform on fractional kinetic equation pertaining to the generalized Galue type Struve function, Adv. Math. Phys. 2019 (2019), Article ID 5074039, 8 pages. https://doi.org/10.1155/2019/5074039

[8]   O. Khan, N. Khan, D. Baleanu and K. S. Nisar, Computable solution of fractional kinetic equations using Mathieu-type series, Adv. Difference Equ. 2019(234) (2019). https://doi.org/10.1186/s13662-019-2167-4

[9]   D. Kumar, J. Choi and H. M. Srivastava, Solution of a general family of fractional kinetic equations associated with the Mittag-Leffler function, Nonlinear Funct. Anal. Appl. 23(3) (2018), 455–471.

[10]   S. D. Purohit and F. Ucar, An application of q-Sumudu transform for fractional q-kinetic equation, Turkish J. Math. 42 (2018), 726–734. https://doi:10.3906/mat-1703-7

[11]   D. L. Suthar, D. Kumar and H. Habenom, Solutions of fractional kinetic equation associated with the generalized multiindex Bessel function via Laplace-transform, Differ. Equ. Dyn. Syst. 2019 (2019). https://doi.org/10.1007/s12591-019-00504-9.

[12]   D. L. Suthar, S. D. Purohit and S. Araci, Solution of fractional kinetic equations associated with the (p,q)-Mathieu-type series, Discrete Dyn. Nat. Soc. 2020 (2020), Article ID 8645161, 7 pages. https://doi.org/10.1155/2020/8645161

[13]   J. Choi and D. Kumar, Solutions of generalized fractional kinetic equations involving Aleph functions, Math. Commun. 20 (2015), 113–123.

[14]   A. Chouhan, S. D. Purohit and S. Srivastava, An alternative method for solving generalized differential equations of fractional order, Kragujevac J. Math. 37(2) (2013), 299–306.

[15]   D. Kumar, S. D. Purohit, A. Secer and A. Atangana, On generalized fractional kinetic equations involving generalized Bessel function of the first kind, Math. Probl. Eng. 2015 (2015), Article ID 289387, 7 pages. https://doi.org/10.1155/2015/289387

[16]   H. J. Haubold and A. M. Mathai, The fractional kinetic equation and thermonuclear functions, Astrophys. Space Sci. 327 (2000), 53–63. https://doi.org/10.1023/A:1002695807970

[17]   R. K. Saxena and S. L. Kalla, On the solutions of certain fractional kinetic equations, Appl. Math. Comput. 199 (2008), 504–511. https://doi.org/10.1016/j.amc.2007.10.005

[18]   R. K. Saxena, A. M. Mathai and H. J. Haubold, On fractional kinetic equations, Astrophys. Space Sci. 282 (2002), 281–287. https://doi.org/10.1023/A:1021175108964

[19]   R. K. Saxena, A. M. Mathai and H. J. Haubold, On generalized fractional kinetic equations, Phys. A 344 (2004), 657–664. https://doi.org/10.1016/j.physa.2004.06.048

[20]   A. M. Mathai, R. K. Saxena and H. J. Haubold, The H-Functions: Theory and Applications, Springer, New York, 2010. https://doi.org/10.1007/978-1-4419-0916-9

[21]   H. M. Srivastava, M. A. Chaudhary and R. P. Agarwal, The incomplete Pochhammer symbols and their applications to hypergeometric and related functions, Integral Transforms Spec. Funct. 23 (2012), 659–683. https://doi.org/10.1080/10652469.2011.623350

[22]   H. M. Srivastava, R. K. Saxena and R. K. Parmar, Some families of the incomplete H-functions and the incomplete H-functions and associated integral transforms and operators of fractional calculus with applications, Russ. J. Math. Phys. 25(1) (2018), 116–138. https://doi.org/10.1134/S1061920818010119

[23]   H. M. Srivastava, A contour integral involving Fox’s H-function, Indian J. Math. 14 (1972), 1–6. https://doi.org/10.12691/ajams-5-1-3.

[24]   K. S. Nisar, S. D. Purohit and S. R. Mondal, Generalized fractional kinetic equations involving generalized Struve function of the first kind, Journal of King Saud University - Science 28(2) (2016), 167–171. https://doi.org/10.1016/j.jksus.2015.08.005