Browsing by Author "Bhatter, Sanjay"

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Citation Count: Bhatter, Sanjay...et al. (2023). "A generalized study of the distribution of buffer over calcium on a fractional dimension", Applied Mathematics In Science And Engineering, Vol. 31, No. 1
A generalized study of the distribution of buffer over calcium on a fractional dimension
(2023) Bhatter, Sanjay; Jangid, Kamlesh; Kumawat, Shyamsunder; Purohit, Sunil Dutt; Baleanu, Dumitru; Suthar, D. L.; 56389
Calcium is an essential element in our body and plays a vital role in moderating calcium signalling. Calcium is also called the second messenger. Calcium signalling depends on cytosolic calcium concentration. In this study, we focus on cellular calcium fluctuations with different buffers, including calcium-binding buffers, using the Hilfer fractional advection-diffusion equation for cellular calcium. Limits and start conditions are also set. By combining with intracellular free calcium ions, buffers reduce the cytosolic calcium concentration. The buffer depletes cellular calcium and protects against toxicity. Association, dissociation, diffusion, and buffer concentration are modelled. The solution of the Hilfer fractional calcium model is achieved through utilizing the integral transform technique. To investigate the influence of the buffer on the calcium concentration distribution, simulations are done in MATLAB 21. The results show that the modified calcium model is a function of time, position, and the Hilfer fractional derivative. Thus the modified Hilfer calcium model provides a richer physical explanation than the classical calcium model.
Citation Count: Bhatter, Sanjay...et.al. (2023). "Analysis of the family of integral equation involving incomplete types of <i>Ii> and (<i>Ii>)over-bar-functions", Applied Mathematics In Science And Engineering, Vol.31, No.1
Analysis of the family of integral equation involving incomplete types of Ii> and (Ii>)over-bar-functions
(2023) Bhatter, Sanjay; Jangid, Kamlesh; Kumawat, Shyamsunder; Baleanu, Dumitru; Purohit, Sunil Dutt; 56389
The present article introduces and studies the Fredholm-type integral equation with an incomplete I-function (I/F) and an incomplete (I) over bar -function ((I/F) over bar) in its kernel. First, using fractional calculus and the Mellin transform principle, we solve an integral problem involving IIF. The idea of the Mellin transform and fractional calculus is then used to analyse an integral equation using the incomplete (I) over bar -function. This is followed by the discovery and investigation of several important exceptional cases. This article's general discoveries may yield new integral equations and solutions. The desired outcomes seem to be very helpful in resolving many real-world problems whose solutions represent different physical phenomena. And also, findings help solve introdifferential, fractional differential, and extended integral equation problems.
Citation Count: Bhatter, Sanjay...et al. (2023). "Analysis of the family of integral equation involving incomplete types of I and Ī-functions", Applied Mathematics in Science and Engineering, Vol. 31, No. 1.
Analysis of the family of integral equation involving incomplete types of I and Ī-functions
(2023) Bhatter, Sanjay; Jangid, Kamlesh; Kumawat, Shyamsunder; Baleanu, Dumitru; Suthar, D.L.; Purohit, Sunil Dutt; 56389
The present article introduces and studies the Fredholm-type integral equation with an incomplete I-function (IIF) and an incomplete (Formula presented.) -function (I (Formula presented.) F) in its kernel. First, using fractional calculus and the Mellin transform principle, we solve an integral problem involving IIF. The idea of the Mellin transform and fractional calculus is then used to analyse an integral equation using the incomplete (Formula presented.) -function. This is followed by the discovery and investigation of several important exceptional cases. This article's general discoveries may yield new integral equations and solutions. The desired outcomes seem to be very helpful in resolving many real-world problems whose solutions represent different physical phenomena. And also, findings help solve introdifferential, fractional differential, and extended integral equation problems.
Citation Count: Jangid, Kamlesh...et al. (2020). "Some fractional calculus findings associated with the incomplete I-functions", Advances in Difference Equations, vol. 2020, No. 1.
Some fractional calculus findings associated with the incomplete I-functions
(2020) Jangid, Kamlesh; Bhatter, Sanjay; Meena, Sapna; Baleanu, Dumitru; Al Qurashi, Maysaa; Purohit, Sunil Dutt; 56389
In this article, several interesting properties of the incomplete I-functions associated with the Marichev-Saigo-Maeda (MSM) fractional operators are studied and investigated. It is presented that the order of the incomplete I-functions increases about the utilization of the above-mentioned operators toward the power multiple of the incomplete I-functions. Further, the Caputo-type MSM fractional order differentiation for the incomplete I-functions is studied and investigated. Saigo, Riemann-Liouville, and Erdelyi-Kober fractional operators are also discussed as specific cases.