Generalization of Katugampola fractional kinetic equation involving incomplete H-function

Document Type : Research Paper

Authors

1 Department of Mathematics, Malaviya National Institute of Technology Jaipur, India.

2 Department of HEAS (Mathematics), Rajasthan Technical University, India. Department of Computer Science and Mathematics, Lebanese American University, Beirut, Lebanon.

Abstract

In this article, Katugampola fractional kinetic equation (KE) has been expressed in terms of polynomials along with incomplete H-function, incomplete Meijer’s G-function, incomplete Fox-Wright function, and incomplete generalized hypergeometric function, weighing the novel significance of the fractional KE that appear in a variety of scientific and engineering scenarios. τ-Laplace transform is used to solve the Kathugampola fractional KE. The obtained solutions have been presented with some real values and the simulation was done via MATLAB. Furthermore, the numerical and graphical interpretations are also mentioned to illustrate the main results. Each of the obtained conclusions is of a general nature and is capable of generating the solutions to several fractional KE.

Keywords

Main Subjects

References

  • [1] T. Abdeljawad, On conformable fractional calculus, J. Comput. Appl. Math., 279 (2015), 57–66.
  • [2] T. Abdeljawad, S. Rashid, Z. Hammouch, and Y. M. Chu, Some new local fractional inequalities associated with generalized (s,m)-convex functions and applications, Adv. Differ. Equ., 1 (2020), 406.
  • [3] P. Agarwal, M. Chand, and G. Singh, Certain fractional kinetic equations involving the product of generalized k-Bessel function, Alex. Eng. J., 4 (2016), 3053–3059.
  • [4] A. Akgl, E. lgl, N. Sakar, B. Bilgi, and A. Eker, New applications of the new general integral transform method with different fractional derivatives, Alex. Eng. J., 80 (2023), 498-505.
  • [5] S. Bhatter, Nishant, and Shyamsunder, Mathematical model on the effect of environmental pollution on biological populations, Advances in Mathematical Modelling, Applied Analysis and Computation, Springer Nature Switzerland, 666 (2023), 488–496.
  • [6] V.B.L. Chaurasia and S.C. Pandey, On the new computable solution of the generalized fractional kinetic equations involving the generalized function for the fractional calculus and related functions, Astrophys. Space Sci., 3 (317) (2008), 213–219.
  • [7] S. B. Chen, S. Rashid, M. A. Noor, Z. Hammouch, and Y. M. Chu, New fractional approaches for n-polynomial P-convexity with applications in special function theory, Adv. Differ. Equ., 1 (2020), 543, 1–31.
  • [8] J. Choi and D. Kumar, Solutions of generalized fractional kinetic equations involving Aleph functions, Math. Commun., 1(20) (2015), 113–123.
  • [9] G. A. Dorrego and D. Kumar, A generalization of the kinetic equation using the Prabhakar-type operators, Honam Math. J., 3(39) (2017), 401–416.
  • [10] B. K. Dutta, L. K. Arora, and J. Borah, On the solution of fractional kinetic equation, Gen. Math. Notes, 1(6) (2011), 40–48.
  • [11] M. Ghasemi, M. Samadi, E. Soleimanian, and K. W. Chau, A comparative study of black-box and white-box data-driven methods to predict landfill leachate permeability, Environ. Monit. Assess., 7(195) (2023), 862.
  • [12] Y. Gu, S. Malmir, J. Manafian, O. A. Ilhan, A. A. Alizadeh, and A. J. Othman, Variety interaction between k-lump and k-kink solutions for the (3+ 1)-D Burger system by bilinear analysis, Results Phys., 43 (2022), 106032.
  • [13] M. S. Hashemi, A. Akgl, A. M. Hassan, and M. Bayram, A method for solving the generalized Camassa-Choi problem with the Mittag-Leffler function and temporal local derivative, Alex. Eng. J., 81 (2023), 437-443.
  • [14] H. J. Haubold and A. M. Mathai, The fractional kinetic equation and thermonuclear functions, Astrophys. Space Sci., 1(273) (2000), 53–63.
  • [15] K. Jangid, S. D. Purohit, K. S. Nisar, and S. Araci, Generating functions involving the incomplete H-functions, Analysis, 4(41) (2021), 239–244.
  • [16] K. Jangid, S. D. Purohit, R. Agarwal, and R. P. Agarwal, On the generalization of fractional kinetic equation comprising incomplete H-function, Kragujevac J. Math., 5(47) (2023), 701–712.
  • [17] F. Jarad and T. Abdeljawad, A modified Laplace transform for certain generalized fractional operators, Results Nonlinear Anal., 2(1) (2018), 88–98.
  • [18] U. N. Katugampola, New approach to a generalized fractional integral, Appl. Math. Comput., 3 (218) (2011), 860–865.
  • [19] S. Kumar and A. Atangana, A numerical study of the nonlinear fractional mathematical model of tumor cells in presence of chemotherapeutic treatment, Int. J. Biomath, 03 (13) (2020), 2050021.
  • [20] I. U. Khan, S. Mustafa, A. Shokri, S. Li, A. Akgl, and A. Bariq, The stability analysis of a nonlinear mathematical model for typhoid fever disease, Sci. Rep., 13(1) (2023), 15284.
  • [21] M. Lakestani, J. Manafian, A. R. Najafizadeh, and M. Partohaghighi, Some new soliton solutions for the nonlinear the fifth-order integrable equations, Comput. methods differ. equ., 10(2) (2022), 445-460.
  • [22] J. Manafian and M. Lakestani, Application of tan(φ/2)-expansion method for solving the BiswasMilovic equation for Kerr law nonlinearity, Optik, 127(4) (2016), 2040-2054.
  • [23] J. Manafian and M. Lakestani, Abundant soliton solutions for the KunduEckhaus equation via tan(φ(ξ))-expansion method, Optik, 127(14) (2016), 5543-5551.
  • [24] J. Manafian and M. Lakestani, Optical soliton solutions for the GerdjikovIvanov model via tan(φ/2)-expansion method, Optik, 127(20) (2016), 9603-9620.
  • [25] J. Manafian and M. Lakestani, N-lump and interaction solutions of localized waves to the (2+ 1)-dimensional variable-coefficient CaudreyDoddGibbonKoteraSawada equation, J. Geom. Phys., 150 (2020), 103598.
  • [26] J. Manafian, L. A. Dawood, and M. Lakestani, New solutions to a generalized fifth-order KdV like equation with prime number p= 3 via a generalized bilinear differential operator, Partial Differ. Equ. Appl. Math., 9 (2024), 100600.
  • [27] A. M. Mathai and R. K. Saxena, The H-function with applications in statistics and other disciplines, John Wiley and Sons, New York, NY, USA, 1978.
  • [28] G. Mittag-Leffler, Sur la representation analytique dune branche uniforme dune fonction monogene, Acta Math., 1(29) (1905), 101–181.
  • [29] E. Mittal, D. Sharma, and S. D. Purohit, Katugampola kinetic fractional equation with its solution, Results Nonlinear Anal., 3(5) (2022), 325–336.
  • [30] E. W. Montroll and G. H. Weiss, Random walks on lattices, II, J. Math. Phys., 2(6) (1965), 167–181.
  • [31] R. R. Nigmatullin, On the theory of relaxation for systems with remnant memory, Phys. Status Solidi (b), 1(124) (1984), 389–393.
  • [32] A. I. Saichev and G. M. Zaslavsky, Fractional kinetic equations: solutions and applications, Chaos, 4(7) (1997), 753–764.
  • [33] M. Samadi, H. Sarkardeh, and E. Jabbari, Explicit data-driven models for prediction of pressure fluctuations occur during turbulent flows on sloping channels, Stoch. Environ. Res. Risk. Assess., 34 (2020), 691–707.
  • [34] R. K. Saxena and S. L. Kalla, On the solutions of certain fractional kinetic equations, Appl. Math. Comput., 2(199) (2008), 504–511.
  • [35] H. M. Srivastava and N. P. Singh, The integration of certain products of the multivariable H-function with a general class of polynomials, Rend. Circ. Mat. Palermo, 2(32) (1983), 157–187.
  • [36] H. M. Srivastava, M. A. Chaudhry, and R.P. Agarwal, The incomplete pochhammer symbols and their applications to hypergeometric and related functions, Integral Transforms Spec. Funct., 9(23) (2012), 659–683.
  • [37] 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 (2018), 116–138.
  • [38] S. K. Vandrangi, Aerodynamic characteristics of NACA 0012 airfoil by CFD analysis, J. Airl. Oper. Aviat. Manag., 1(1) (2022), 1–8.
  • [39] G. Velidi, Pressure and velocity variation in remote-controlled plane using CFD analysis, J. Airl. Oper. Aviat. Manag., 1(1) (2022), 9–18.
  • [40] G. H. Weiss, Aspects and applications of the random walk, North Holland, AmsterdamNew YorkOxford, 1994.
  • [41] M. Zhang, X. Xie, J. Manafian, O. A. Ilhan, and G. Singh, Characteristics of the new multiple rogue wave solutions to the fractional generalized CBS-BK equation, J. Adv. Res., 38 (2022), 131-142.
Computational Methods for Differential Equations
Volume 12, Issue 4
October 2024
Pages 842-856

Files

History

  • Receive Date: 27 June 2023
  • Revise Date: 19 January 2024
  • Accept Date: 09 February 2024

Share

How to cite

Statistics