Browsing by Author "Purohit, Sunil Dutt"

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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: Mishra, A.M...et al. (2019). "Certain Results Comprising the Weighted Chebyshev Function Using Pathway Fractional Integrals",Mathematics, Vol. 7, No. 10.
Certain Results Comprising the Weighted Chebyshev Function Using Pathway Fractional Integrals
(MDPI AG, 2020) Mishra, Aditya Mani; Baleanu, Dumitru; Tchier, Fairouz; Purohit, Sunil Dutt; 56389
An analogous version of Chebyshev inequality, associated with the weighted function, has been established using the pathway fractional integral operators. The result is a generalization of the Chebyshev inequality in fractional integral operators. We deduce the left sided Riemann Liouville version and the Laplace version of the same identity. Our main deduction will provide noted results for an appropriate change to the Pathway fractional integral parameter and the degree of the fractional operator.
Citation Count: Agrawal, Priyanka...et.al. (2023). "Exploration Of Casson Fluid-Flow Along Exponential Heat Source In A Thermally Stratified Porous Media", Thermal Science, Vol.27, No.SI, pp.S29-S38.
Exploration Of Casson Fluid-Flow Along Exponential Heat Source In A Thermally Stratified Porous Media
(2023) Agrawal, Priyanka; Dadheech, Praveen Kumar; Jat, Ram Niwas; Baleanu, Dumitru; Purohit, Sunil Dutt; 56389
Objective of the present investigation is intended to study the MHD Casson fluids flow through an exponentially stretching surface. This free convective flow is in-vestigated in thermally stratified porous medium. Also viscosity along with thermal conductivity is varying with temperature. With the exponential decay for the inter-nal heat generation in the region and buoyancy force, the natural-convection is induced. Then the transformed set of equations of the flow after applying suitable similarity solutions were encountered by Shooting Technique in conjunction with the fourth ordered Runge-Kutta method. Outputs illustrates that with increased viscosity parameter an increasing velocity profile is noticed but a decrement is observed for temperature field in entire domain and near the wall for temperature gradient profile. Also with increased Casson fluids parameter decreasing velocity profile is noticed but an increment is observed for temperature field in entire do-main and for temperature gradient profile near the wall.
Citation Count: Baleanu, D., Purohit, S.D., Prajapati, J.C. (2016). Integral inequalities involving generalized Erdelyi-Kober fractional integral operators. Open Mathematics, 14, 89-99. http://dx.doi.org/10.1515/math-2016-0007
Integral inequalities involving generalized Erdelyi-Kober fractional integral operators
(De Gruyter Open Ltd., 2016) Baleanu, Dumitru; Purohit, Sunil Dutt; Prajapati, Jyotindra
Using the generalized Erdelyi-Kober fractional integrals, an attempt is made to establish certain new fractional integral inequalities, related to the weighted version of the Chebyshev functional. The results given earlier by Purohit and Raina (2013) and Dahmani et al. (2011) are special cases of results obtained in present paper.
Citation Count: Purohit, Sunil Dutt; Baleanu, Dumitru; Jangid, Kamlesh (2021). "On the solutions for generalised multiorder fractional partial differential equations arising in physics", Mathematical Methods in the Applied Sciences.
On the solutions for generalised multiorder fractional partial differential equations arising in physics
(2021) Purohit, Sunil Dutt; Baleanu, Dumitru; Jangid, Kamlesh; 56389
In this article, we have studied solutions of a generalised multiorder fractional partial differential equations involving the Caputo time-fractional derivative and the Riemann–Liouville space fractional derivatives using Laplace–Fourier transform technique. Proposed generalised multiorder fractional partial differential equation is reducible to Schrödinger equation, wave equation and diffusion equation in a more general sense, and hence, solutions of these equations are specifically noted. Not only this, solutions of equation proposed in the stochastic resetting theory in the context of Brownian motion can also be found in a general regime.
Citation Count: Agrawal, Priyanka...et al. (2021). "Radiative MHD hybrid-nanofluids flow over a permeable stretching surface with heat source/sink embedded in porous medium", International Journal of Numerical Methods for Heat and Fluid Flow, Vol. 31, No. 8, pp. 2818-2840.
Radiative MHD hybrid-nanofluids flow over a permeable stretching surface with heat source/sink embedded in porous medium
(2021) Agrawal, Priyanka; Dadheech, Praveen Kumar; Jat, R.N.; Baleanu, Dumitru; Purohit, Sunil Dutt; 56389
Purpose: The purpose of this paper is to study the comparative analysis between three hybrid nanofluids flow past a permeable stretching surface in a porous medium with thermal radiation. Uniform magnetic field is applied together with heat source and sink. Three set of different hybrid nanofluids with water as a base fluid having suspension of Copper-Aluminum Oxide (Formula presented.), Silver-Aluminum Oxide (Formula presented.) and Copper-Silver (Formula presented.) nanoparticles are considered. The Marangoni boundary condition is applied. Design/methodology/approach: The governing model of the flow is solved by Runga–Kutta fourth-order method with shooting technique, using appropriate similarity transformations. Temperature and velocity field are explained by the figures for many flow pertinent parameters. Findings: Almost same behavior is observed for all the parameters presented in this analysis for the three set of hybrid nanofluids. For increased mass transfer wall parameter ((Formula presented.)) and Prandtl Number (Pr), heat transfer rate cuts down for all three sets of hybrid nanofluids, and reverse effect is seen for radiation parameter (R), and heat source/sink parameter ((Formula presented.)). Practical implications: The thermal conductivity of hybrid nanofluids is much larger than the conventional fluids; thus, heat transfer efficiency can be improved with these fluids and its implications can be seen in the fields of biomedical, microelectronics, thin-film stretching, lubrication, refrigeration, etc. Originality/value: The current analysis is to optimize heat transfer of three different radiative hybrid nanofluids ((Formula presented.), (Formula presented.) and (Formula presented.)) over stretching surface after applying heat source/sink with Marangoni convection. To the best of the authors’ knowledge, this work is new and never published before.
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.
Citation Count: Rahman, Gauhar...et al. (2017). "The extended Mittag-Leffler function via fractional calculus", Journal Of Nonlinear Sciences And Applications, Vol.10, No.8, pp.4244-4253.
The extended Mittag-Leffler function via fractional calculus
(Int Scientific Research Publications, 2017) Rahman, Gauhar; Baleanu, Dumitru; Al Qurashi, Maysaa Mohamed; Purohit, Sunil Dutt; Mubeen, Shahid; Arshad, Muhammad
In this study, our main attempt is to introduce fractional calculus (fractional integral and differential) operators which contain the following new family of extended Mittag-Leffler function: E-alpha,beta(gamma;q,c) (z) = Sigma(infinity)(n=0) B-p (gamma + nq, c - gamma)(c)(nq) z(n)/B(gamma, c - gamma)Gamma(alpha n + beta) n!' (z,beta,gamma is an element of C), as its kernel. We also investigate a certain number of their consequences containing the said function in their kernels.