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Your search keyword '"Dubey, Ved Prakash"' showing total 4 results
Start Over Author "Dubey, Ved Prakash" Topic caputo fractional derivatives
4 results on '"Dubey, Ved Prakash"'

1. Numerical solution of time-fractional three-species food chain model arising in the realm of mathematical ecology.

Author

Dubey, Ved Prakash, Kumar, Rajnesh, and Kumar, Devendra

Subjects
*ANALYTICAL solutions, *CAPUTO fractional derivatives, *FRACTIONAL differential equations, *ECOLOGY, *FOOD chains
Abstract

This research paper implements the fractional homotopy analysis transform technique to compute the approximate analytical solution of the nonlinear three-species food chain model with time-fractional derivatives. The offered technique is a fantastic blend of homotopy analysis method (HAM) and Laplace transform (LT) operator and has been used fruitfully in the numerical computation of various fractional differential equations (FDEs). This paper involves the fractional derivatives of Caputo style. The numerical solutions of this selected fractional-order food chain model are evaluated by making use of the associated initial conditions. It is revealed by the adopting procedure that the more desirable estimation of the solution can be easily acquired through the calculation of some number of iteration terms only — a fact which authenticates the easiness and soundness of the suggested hybrid scheme. The variations of fractional order of time derivative on the solutions for different specific cases have been depicted through graphical presentations. The outcomes demonstrated through the graphs expound that the adopted scheme is very fantastic and accurate. [ABSTRACT FROM AUTHOR]

Published
2020
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2. An efficient computational scheme for nonlinear time fractional systems of partial differential equations arising in physical sciences.

Author

Dubey, Ved Prakash, Kumar, Rajnesh, Kumar, Devendra, Khan, Ilyas, and Singh, Jagdev

Subjects
*PARTIAL differential equations, *PHYSICAL sciences, *FRACTIONAL powers, *POWER series, *CAPUTO fractional derivatives
Abstract

In this paper, we broaden the utilization of a beautiful computational scheme, residual power series method (RPSM), to attain the fractional power series solutions of nonhomogeneous and homogeneous nonlinear time-fractional systems of partial differential equations. This paper considers the fractional derivatives of Caputo-type. The approximate solutions of given systems of equations are calculated through the utilization of the provided initial conditions. This iterative scheme generates the fast convergent series solutions with conveniently determinable components. The implementation of this numerical scheme clearly exhibits its effectiveness, reliability and easiness regarding the procedure of the solution, as well as its better approximation. The repercussions of the fractional order of Caputo derivatives on solutions are depicted through graphical presentations for various particular cases. [ABSTRACT FROM AUTHOR]

Published
2020
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3. A computational study of fractional model of atmospheric dynamics of carbon dioxide gas.

Author

Dubey, Ved Prakash, Dubey, Sarvesh, Kumar, Devendra, and Singh, Jagdev

Subjects
*ATMOSPHERIC models, *CAPUTO fractional derivatives, *POPULATION, *ATMOSPHERIC circulation, *CARBON dioxide, *ATMOSPHERIC carbon dioxide
Abstract

In this paper, a fractional order nonlinear mathematical model describing the dynamics of atmospheric concentration of CO 2 is investigated and studied through the application of a semi-analytical homotopy scheme combined with Sumudu transform and homotopy polynomials. This study examines the consequences of the variations of forest biomass and human population on the dynamics of the concentration of CO 2 gas in the atmosphere. The Caputo fractional derivatives are engaged in this study. The computational work shows that the evaluated iterative terms are adequate for the refined approximations of the solutions for a fractional model of dynamics of atmospheric concentration of CO 2 , and thus authenticate the computational strength of the employed scheme. The variational behavior of concentration of CO 2 , forest biomass, and human population are demonstrated through the graphical presentation regarding the changing values of fractional order derivatives and time t. Moreover, this study also examines the analysis of obtained solutions for a fractional model in view of uniqueness and convergence. [ABSTRACT FROM AUTHOR]

Published
2021
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4. A hybrid analytical scheme for the numerical computation of time fractional computer virus propagation model and its stability analysis.

Author

Dubey, Ved Prakash, Kumar, Rajnesh, and Kumar, Devendra

Subjects
*CAPUTO fractional derivatives, *COMPUTER viruses, *STABILITY criterion, *COMPUTER simulation, *ANALYTICAL solutions
Abstract

• We examine a fractional computer virus propagation model. • The fractional Routh–Hurwitz stability criterion is used to analyze the local stability of the model. • The HPTM is employed to perform the numerical simulation for the model. • The impact of order of Caputo fractional derivative is presented in the form of graphs. In this paper, we present an application of the homotopy perturbation transform method to compute the approximate analytical solution of the nonlinear fractional order computer virus propagation (CVP) model. The fractional derivatives are used in Caputo sense. The proposed approximate method generates the numerical solution in the shape of a rapid convergent series by utilizing the provided initial conditions. The main purpose of the paper is to analyze the effect of variation of fractional order α on the meeting time of susceptible, infected and recovered computers. Moreover, the local stability analysis of the fractional order computer virus model is also presented using Routh–Hurwitz stability criterion. [ABSTRACT FROM AUTHOR]

Published
2020
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