Browsing by Author "Purohit, S. D."

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Citation Count: Habenom, Haile;...et.al. (2021). "A Numerical Simulation on the Effect of Vaccination and Treatments for the Fractional Hepatitis B Model", Journal Of Computational And Nonlinear Dynamics, Vol.16, No.1.
A Numerical Simulation on the Effect of Vaccination and Treatments for the Fractional Hepatitis B Model
(2021) Habenom, Haile; Suthar, D. L.; Baleanu, D.; Purohit, S. D.; 56389
The aim of this paper is to develop a fractional order mathematical model for describing the spread of hepatitis B virus (HBV). We also provide a rigorous mathematical analysis of the stability of the disease-free equilibrium (DFE) and the endemic equilibrium of the system based on the basic reproduction number. Here, the infectious disease HBV model is described mathematically in a nonlinear system of differential equations in a caputo sense, and hence, Jacobi collocation method is used to reduce into a system of nonlinear equations. Finally, Newton Raphson method is used for the systems of nonlinear equations to arrive at an approximate solution and matlab 2018 has helped us to simulate the nature of each compartment and effects of the possible control strategies (i.e., vaccination and isolation).
Citation Count: Baleanu, D.; Agarwal, P.; Purohit, S. D. "Certain Fractional Integral Formulas Involving the Product of Generalized Bessel Functions", Scientific World Journal, (2013)
Certain Fractional Integral Formulas Involving the Product of Generalized Bessel Functions
(Hindawi LTD, 2013) Baleanu, Dumitru; Agarwal, Ravi P.; Purohit, S. D.; 56389
We apply generalized operators of fractional integration involving Appell's function F-3(.) due to Marichev-Saigo-Maeda, to the product of the generalized Bessel function of the first kind due to Baricz. The results are expressed in terms of the multivariable generalized Lauricella functions. Corresponding assertions in terms of Saigo, Erdelyi-Kober, Riemann-Liouville, and Weyl type of fractional integrals are also presented. Some interesting special cases of our two main results are presented. We also point out that the results presented here, being of general character, are easily reducible to yield many diverse new and known integral formulas involving simpler functions.
Citation Count: Suthar, D.L...et al. (2020). "Certain K-Fractional Calculus Operators and Image Formulas of K-Struve Function",Aims Mathematics, Vol. 5, No. 3, pp. 1706-1719.
Certain K-Fractional Calculus Operators and Image Formulas of K-Struve Function
(American Institute of Mathematical Sciences, 2020) Suthar, D. L.; Baleanu, Dumitru; Purohit, S. D.; Uçar, Faruk; 56389
In this article, the Saigo’s k-fractional order integral and derivative operators involving k-hypergeometric function in the kernel are applied to the k-Struve function; outcome are expressed in the term of k-Wright function, which are used to present image formulas of integral transforms including beta transform. Also special cases related to fractional calculus operators and Struve functions are considered.
Citation Count: Baleanu, Dimitru; Purohit, S. D., "Chebyshev Type Integral Inequalities Involving the Fractional Hypergeometric Operators", Abstract and Applied Analysis, (2014).
Chebyshev Type Integral Inequalities Involving the Fractional Hypergeometric Operators
(Hindawi LTD, 2014) Baleanu, Dumitru; Purohit, S. D.; 56389
By making use of the fractional hypergeometric operators, we establish certain new fractional integral inequalities for synchronous functions which are related to the weighted version of the Chebyshev functional. Some consequent results and special cases of the main results are also pointed out.
Citation Count: Agarwal, Ritu...et al. (2020). "Existence and uniqueness of miscible flow equation through porous media with a non singular fractional derivative", AIMS Mathematics, Vol. 5, No. 2, pp. 1062-1073.
Existence and uniqueness of miscible flow equation through porous media with a non singular fractional derivative
(2020) Agarwal, Ritu; Yadav, Mahaveer Prasad; Baleanu, Dumitru; Purohit, S. D.; 56389
In this paper, we discuss the phenomenon of miscible flow with longitudinal dispersion in porous media. This process simultaneously occur because of molecular diffusion and convection. Here, we analyze the governing differential equation involving Caputo-Fabrizio fractional derivative operator having non singular kernel. Fixed point theorem has been used to prove the uniqueness and existence of the solution of governing differential equation. We apply Laplace transform and use technique of iterative method to obtain the solution. Few applications of the main result are discussed by taking different initial conditions to observe the effect on derivatives of different fractional order on the concentration of miscible fluids.
Citation Count: Baleanu, D., Kumar, D., Puhorit, S.D. (2016). Generalized fractional integrals of product of two H-functions and a general class of polynomials. International Journal Of Computer Mathematics, 93(8), 1320-1329. http://dx.doi.org/10.1080/00207160.2015.1045886
Generalized fractional integrals of product of two H-functions and a general class of polynomials
(Taylor&Francis Ltd, 2016) Baleanu, Dumitru; Kumar, Dinesh; Purohit, S. D.
The purpose of this paper is to compute two unified fractional integrals involving the product of two H-functions, a general class of polynomials and Appell function F-3. These integrals are further applied in proving two theorems on Saigo-Maeda fractional integral operators. Some consequent results and special cases are also pointed out in the concluding section
Citation Count: Nisar, K. S...et al. (2016). "Generalized k-Mittag-Leffler function and its composition with pathway integral operators" Journal of Nonlinear Sciences and Applications, Vol. 9, No. 6, pp. 3519-3526.
Generalized k-Mittag-Leffler function and its composition with pathway integral operators
(Int Scientific Research Publications, 2016) Nisar, Kottakkaran Sooppy; Purohit, S. D.; Abouzaid, M. S.; Al Qurashi, Maysaa Mohamed; Baleanu, Dumitru; 56389
Our purpose in this paper is to consider a more generalized form of the Mittag-Leffler function. For this newly defined function, we obtain certain composition formulas with pathway fractional integral operators. We also point out some important special cases of the main results. (C) 2016 All rights reserved.
Citation Count: Baleanu, Dumitru; Purohit, S.D.; Ucar, F. "On gruss type integral inequality involving the Saigo's fractional integral operators", Journal of Computational Analysis and Applications, Vol.19, No.3, pp.480-489, (2017).
On gruss type integral inequality involving the Saigo's fractional integral operators
(Eudoxus Press, 2015) Baleanu, Dumitru; Purohit, S. D.; Uçar, Faruk; 56389
Using Saigo's fractional integral operators, we establish a generalized version of the Gruss type integral inequality related to the bounded integrable functions, whose bounds are integrable functions. Some special cases of our results are also considered.