Impact of fractional order on reaction rates: Solutions to kinetic equations with incomplete $\aleph$-function

-, Shyamsunder; Gangwar, Diksha

doi:10.22034/cmde.2025.61995.2704

فهرست نشریات دارای اعتبار وزارت علوم، تحقیقات و فناوری

تعداد نشریات	45
تعداد شماره‌ها	1,497
تعداد مقالات	18,256
تعداد مشاهده مقاله	59,160,010
تعداد دریافت فایل اصل مقاله	20,612,789

	Impact of fractional order on reaction rates: Solutions to kinetic equations with incomplete $\aleph$-function
Computational Methods for Differential Equations
مقاله 5، دوره 14، شماره 2، تیر 2026، صفحه 581-589 اصل مقاله (407.44 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22034/cmde.2025.61995.2704
نویسندگان
Shyamsunder -^* ¹؛ Diksha Gangwar²
¹Department of Mathematics, SRM University Delhi-NCR, Sonepat-131029, Haryana, India.
²Department of Applied Mathematics, M. J. P. Rohilkhand University, Bareilly-243006, Uttar Pradesh, India.
چکیده
In this study, we investigate the significance of fractional kinetic equations in emerging a wide range of problems in science and engineering. Specifically, we derive a fractional kinetic equation solution involving the incomplete $\aleph$-function using a well-established integral transform technique. To illustrate the impact of the fractional integral operator’s order on reaction rates, we present several graphical results, highlighting the influence of fractional calculus on the system’s dynamics.
کلیدواژه‌ها
Laplace transform؛ Riemann-Liouville fractional integral؛ Kinetic equation؛ Incomplete $\aleph$-function

مراجع
[1] J. C. Arya, Generalized fractional kinetic equations involving incomplete Aleph-function, Int. J. Math. Res., 12(1) (2023), 1–8. [2] M. K. Bansal, D. Kumar, K. S. Nisar, and J. Singh, Certain fractional calculus and integral transform results of incomplete ℵ-functions with applications, Math. Meth. Appl. Sci., 43(8) (2020), 5602–5614. [3] M. K. Bansal and D. Kumar, On the integral operators pertaining to a family of incomplete I-functions, AIMS Math., 5(2) (2020), 1247–1259. [4] S. Bhatter, Nishant, Shyamsunder, S. D. Purohit, and D. L. Suthar, A study of incomplete I-functions relating to certain fractional integral operators, AMSE, 31(1) (2023), 2252996. [5] S. Bhatter, Nishant, Shyamsunder, and S. D. Purohit, Srivastava-Luo-Raina M-transform involving the incomplete I-functions, Comput. Methods Differ. Equ., 12(1) (2024), 159–172. [6] M. A. Chaudhry and S. M. Zubair, On a class of incomplete gamma functions with applications, Chapman and Hall/CRC, Florida, 2001. [7] J. Choi and D. Kumar, Solutions of generalized fractional kinetic equations involving -functions, Math. Commun., 20(1) (2015), 113–123. [8] H. Habenom, D. L. Suthar, and M. Gebeyehu, Application of Laplace transform on fractional kinetic equation pertaining to the generalized Galué type Struve function, Adv. Math. Phys., 2019 (2019). [9] H. J. Haubold and A. M. Mathai, The fractional kinetic equation and thermonuclear functions, Astrophys. Space Sci., 273 (2000), 53–63. [10] K. Jangid, S. D. Purohit, R. Agarwal, and R. P. Agarwal, On the generalization of fractional kinetic equation comprising incomplete H-functions, Kragujevac J. Math., 47(5) (2023), 701–712. [11] A. M. Legendre, Nouvelles methodes pour la determination des orbites des cometes, Courcier, Paris, 1808. [12] Nishant, S. Bhatter, and S. D. Purohit, Generalization of Katugampola fractional kinetic equation involving incomplete H-function, Comput. Methods Differ. Equ., 12(4) (2024), 842–856. [13] S. Panwar, R. M. Pandey, S. D. Purohit, and Shyamsunder, A mathematical analysis of non-linear smoking model via fractional operators, Comput. Methods Differ. Equ., (2024), 1–22, DOI:10.22034/cmde.2024.62331.2738. [14] F. Prym, Uber die gamma function, Math. Ann., 29(2) (1887), 165–182. [15] V. P. Saxena, Formal solution of certain new pair of dual integral equations involving H-functions, Proc. Nat. Acad. Sci. India Sect. A, 52 (1982), 366–375. [16] R. K. Saxena, S. L. Kalla, and R. Saxena, Multivariate analogue of generalized Mittag-Leffler function, Integral Transforms Spec. Funct., 22(7) (2011), 533–548. [17] O. Schlömilch, Handbuch der algebraischen Analysis, Frommann, Germany, 1873. [18] Shyamsunder, Comparative implementation of fractional blood alcohol model by numerical approach, Crit. Rev. Biomed. Eng., 53(2) (2024), 11–19. [19] Shyamsunder, Kritika, and S. D. Purohit, Expansion formulae for incomplete Yang-Yu-W-function with Bessel function, Commun. Calc. Anal. Spec. Funct. Math. Phys., 1(1) (2024), 03–10. [20] Shyamsunder and S. D. Purohit, A novel study of the impact of vaccination on pneumonia via fractional approach, Partial Differ. Equ. Appl. Math., 10 (2024), 100698. [21] H. M. Srivastava, R. K. Saxena, and R. K. Parmar, Some families of the incomplete H-functions and the incomplete H-function and associated integral transforms and operators of fractional calculus with applications, Russ. J. Math. Phys., 25 (2018), 116–138. [22] N. Südland, B. Baumann, and T. F. Nonnenmacher, Open problem: who knows about the Aleph-functions, Fract. Calc. Appl. Anal., 1(4) (1998), 401–402. [23] J. Tannery, Introduction àla théorie des fonctions d’une variable, A. Hermann, France, 1910.
آمار تعداد مشاهده مقاله: 261 تعداد دریافت فایل اصل مقاله: 218

سامانه مدیریت نشریات علمی. قدرت گرفته از سیناوب

پیوندهای مفید

آمار

Impact of fractional order on reaction rates: Solutions to kinetic equations with incomplete $\aleph$-function