Analysis of blood sugar with an incomplete $\aleph$-function

Meena, Manisha

doi:10.22034/cmde.2025.64151.2889

فهرست نشریات دارای اعتبار وزارت علوم، تحقیقات و فناوری

تعداد نشریات	45
تعداد شماره‌ها	1,554
تعداد مقالات	18,950
تعداد مشاهده مقاله	63,892,158
تعداد دریافت فایل اصل مقاله	23,341,332

	Analysis of blood sugar with an incomplete $\aleph$-function
Computational Methods for Differential Equations
مقاله 18، دوره 14، شماره 4، دی 2026، صفحه 1815-1824 اصل مقاله (792.69 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22034/cmde.2025.64151.2889
نویسنده
Manisha Meena^*
Department of Mathematics, Motilal Nehru College, University of Delhi, Delhi, India.
چکیده
Mathematical modeling plays a vital role in understanding complex medical and biological processes. In this study, we develop a mathematical model incorporating the incomplete $\aleph$-function to analyze glucose supply in human blood. The model provides a generalized framework to assess glucose dynamics under varying physiological conditions. Numerical simulations demonstrate the impact of key parameters on glucose distribution, revealing critical thresholds for maintaining optimal glucose levels. The findings offer valuable insights into glucose regulation mechanisms, with potential applications in diabetes management and metabolic health monitoring. The general results reveal several intriguing cases concerning the relevant parameters involved.
کلیدواژه‌ها
Sumudu transform؛ Glucose tolerance test؛ Mellin-Barnes type integral؛ Incomplete $\aleph$-function

مراجع
[1] W. Adel, H. Günerhan, K. S. Nisar, P. Agarwal, and A. El-Mesady, Designing a novel fractional order mathematical model for COVID-19 incorporating lockdown measures, Sci. Rep., 14(1) (2024), 2926. [2] V. Agarwal, M. C. Khatumariya, Shyamsunder, and S. Kumar, Internal blood pressure dynamics: modeling with incomplete ℵ-function and fractional operator, Adv. Math. Sci. Appl., 34(02) (2025), 651–662. [3] D. Albayrak, S. D. Purohit, and U. Faruk, Certain inversion and representation formulas for q-Sumudu transforms, Hacet. J. Math. Stat., 43(5) (2014), 699–713. [4] 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. [5] 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. Methods Appl. Sci., 43(8) (2020), 5602–5614. [6] 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. [7] S. Bhatter, K. Jangid, S. D. Purohit, and Shyamsunder, Determining glucose supply in blood using the incomplete I-function, Differ. Equ. Appl. Math., 10 (2024), 100729. [8] S. Bhatter, S. D. Purohit, and Shyamsunder, Several computational based expansions for incomplete -function using the Leibniz rule, In International Conference on Mathematical Modelling, Applied Analysis and Computation, 953 (2023), 306–314. [9] D. S. Bodkhe and S. K. Panchal, On Sumudu transform of fractional derivatives and its applications to fractional differential equations, Asian J. Math. Comput. Res., 11(1) (2016), 69–77. [10] M. A. Chaudhry and S. M. Zubair, On a class of incomplete gamma functions with applications, Chapman and Hall/CRC, 2001. [11] A. El-Mesady and H. M. Ali, The influence of prevention and isolation measures to control the infections of the fractional chickenpox disease model, Math. Comput. Simul., 226 (2024), 606–630. [12] A. El-Mesady, A. Elsadany, A. Mahdy, and A. Elsonbaty, Nonlinear dynamics and optimal control strategies of a novel fractional-order lumpy skin disease model, J. Comput. Sci., 79 (2024), 102286. [13] A. El-Mesady, O. J. Peter, A. Omame, and F. A. Oguntolu, Mathematical analysis of a novel fractional order vaccination model for tuberculosis incorporating susceptible class with underlying ailment, Int. J. Model. Simul. (2024), 1–25. [14] A. Elsonbaty, M. Alharbi, A. El-Mesady, and W. Adel, Dynamical analysis of a novel discrete fractional lumpy skin disease model, Partial Differ. Equ. Appl. Math., 9 (2024), 100604. [15] M. Higazy, S. A. Alsallami, S. Abdel-Khalek, and A. El-Mesady, Dynamical and structural study of a generalized Caputo fractional order Lotka-Volterra model, Results Phys., 37 (2022), 105478. [16] K. Jangid, S. Bhatter, S. Meena, D. Baleanu, A. M. Qurashi, and S. D. Purohit, Some fractional calculus findings associated with the incomplete I-functions, Adv. Difference Equ., 2020(1) (2020), 265. [17] K. Jangid, S. D. Purohit, K. S. Nisar, and T. Shefeeq, The internal blood pressure equation involving incomplete I-functions, Inf. Sci. Lett., 9(3) (2020), 2. [18] H. Kang, K. Han, and M. Choi, Mathematical model for glucose regulation in the whole-body system, Islets, 4(2) (2012), 84–93. [19] J. N. Kapur, Mathematical models in biology and medicine, Affiliated East-West Press Pvt. Ltd., New Delhi, India, 1985. [20] A. A. Kilbas, H. M. Srivastava, and J. J. Trujillo, Theory and applications of fractional differential equations, Elsevier, 2006. [21] 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. 14(1) (2026), 60-80. [22] A. K. Rathie, A new generalization of generalized hypergeometric functions, Le Math., LII (1997), 297–310. [23] D. Sanyal and A. Maiti, Stochastic variation of concentration in blood glucose, Appl. Sci. Periodical, 2 (1999), 65–67. [24] 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. [25] Shyamsunder, Comparative implementation of fractional blood alcohol model by numerical approach, Crit. Rev. Biomed. Eng., 53(2) (2024), 11–19. [26] 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. [27] Shyamsunder and S. D. Purohit, Generalized Eulerian integrals involving the incomplete I-function, Adv. Math. Sci. Appl., 34(1) (2025), 301–311. [28] Shyamsunder, Solutions of fractional kinetic equation involving incomplete ℵ-function, In International Conference on Computational Modeling and Sustainable Energy, (2025), 215–230. [29] Shyamsunder and D. Gangwar, Impact of fractional order on reaction rates: Solutions to kinetic equations with incomplete -function, Comput. Methods Differ. Equ.,14(2) (2026), 581-589. [30] H. M. Srivastava, K. C. Gupta, and S. P. Goyal, The H-functions of one and two variables, with applications, South Asian Publishers, 1982. [31] H. M. Srivastava, R. K. Saxena, and R. K. Parmar, Some families of the incomplete H-functions and the incomplete $\bar{H}$-functions and associated integral transforms and operators of fractional calculus with applications, Russ. J. Math. Phys., 25(1) (2018), 116–138. [32] N. Südland, B. Baumann, and T. F. Nonnenmacher, Who knows about the ℵ-function, Fract. Calc. Appl. Anal, 1(4) (1998), 401–402. [33] N. Südland, G. Baumann, and T. F. Nonnenmacher, Fractional driftless fokker-planck equation with power-law diffusion coefficients, In Computer Algebra in Scientific Computing CASC 2001, pages 513–528, Springer, 2001. [34] R. Walker and J. R. Type, Diabetes–your questions answered, Dorling Kindersley, 2006. [35] D. H. Wasserman, Four grams of glucose, Am. J. Physiol., 296(1) (2009), E11–E21.
آمار تعداد مشاهده مقاله: 298 تعداد دریافت فایل اصل مقاله: 278

سامانه مدیریت نشریات علمی. قدرت گرفته از سیناوب

پیوندهای مفید

آمار

Analysis of blood sugar with an incomplete $\aleph$-function