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Showing papers by "Doddabhadrappla Gowda Prakasha published in 2019"


Journal ArticleDOI
17 Jan 2019-Chaos
TL;DR: The q-homotopy analysis transform method is applied to the mathematical model of the cancer chemotherapy effect in the sense of Caputo fractional to find some new approximate numerical results for different values of parameters of alpha.
Abstract: In this paper, we apply the q-homotopy analysis transform method to the mathematical model of the cancer chemotherapy effect in the sense of Caputo fractional. We find some new approximate numerical results for different values of parameters of alpha. Then, we present novel simulations for all cases of results conducted by considering the values of parameters of alpha in terms of two- and three-dimensional figures along with tables including critical numerical values.

142 citations


Journal ArticleDOI
TL;DR: In this article, an effective analytical technique called q-homotopy analysis transform method (q-HATM) is demonstrated in order to analyse a fractional model of telegraph equations.
Abstract: An effective analytical technique, called q-homotopy analysis transform method (q-HATM) is demonstrated in order to analyse a fractional model of telegraph equations. Test examples are illustrated to inspect the efficiency of the proposed technique. Numerical solutions are obtained in the form of series. Also, its convergence condition, error estimate and numerical simulation results are discussed. The q-HATM handles and controls a series solution that speedily converges to exact result in a small admissible domain efficiently.

82 citations


Journal ArticleDOI
TL;DR: In this paper, an efficient numerical technique, called q-homotopy analysis transform method (briefly, $$q$$¯¯¯¯ -HATM), is applied to nonlinear Fisher's equation of fractional order.
Abstract: In the present work, an efficient numerical technique, called q-homotopy analysis transform method (briefly, $$q$$ -HATM), is applied to nonlinear Fisher’s equation of fractional order. The homotopy polynomials are employed, in order to handle the nonlinear terms. Numerical examples are illustrated to examine the efficiency of the proposed technique. The suggested algorithm provides the auxiliary parameters $$\hbar$$ and $$n$$ , which help us to control and adjust the convergence region of the series solution. The outcomes of the study reveal that the $$q$$ -HATM is computationally very effective and accurate to analyse nonlinear fractional differential equations.

79 citations


Journal ArticleDOI
TL;DR: In this paper, the authors proposed a solution for fractional Drinfeld-Sokolov-Wilson equation using q -homotopy analysis transform method (q-HATM).
Abstract: The pivotal aim of the present work is to find the solution for fractional Drinfeld–Sokolov–Wilson equation using q -homotopy analysis transform method ( q -HATM). The proposed technique is graceful amalgamations of Laplace transform technique with q-homotopy analysis scheme, and fractional derivative defined with Atangana-Baleanu (AB) operator. The fixed point hypothesis considered in order to demonstrate the existence and uniqueness of the obtained solution for the proposed fractional order model. In order to validate and illustrate the efficiency of the future technique, we analysed the projected model in terms of fractional order. Meanwhile, the physical behaviour of the q -HATM solutions have been captured in terms of plots for diverse fractional order and the numerical simulation is also demonstrated. The achieved results illuminate that, the future algorithm is easy to implement, highly methodical as well as effective and very accurate to analyse the behaviour of coupled nonlinear differential equations of fractional order arisen in the connected areas of science and engineering.

66 citations


Journal ArticleDOI
TL;DR: In this paper, an approximated analytical solution for the fractional smoking epidemic model with the aid of a novel technique called q-homotopy analysis transform method (q-HATM) is presented.
Abstract: The pivotal aim of the present work is to obtain an approximated analytical solution for the fractional smoking epidemic model with the aid of a novel technique called q-homotopy analysis transform method (q-HATM). The considered nonlinear mathematical model has been effectively employed to elucidate the evolution of smoking in a population and its impact on public health in a community. We find some new approximate solutions in a series form, which converges rapidly, and the proposed algorithm provides auxiliary parameters, which are very reliable and feasible in controlling the convergence of obtained approximate solutions. Further, we present novel simulations for all cases of results to validate the applicability and effectiveness of proposed scheme. The outcomes of the study reveal that the q-HATM is computationally very effective to analyse nonlinear fractional differential equations arises in daily life problems.

55 citations


Journal ArticleDOI
TL;DR: In this paper, the dynamics of fractional mathematical model of the hepatitis E virus using the fractional Atangana-Baleanu (AB) derivative is analyzed and the existence and uniqueness of the solution obtained for the proposed model with the help of the fixed-point hypothesis.
Abstract: The pivotal aim of the present work is to analyse the dynamics of fractional mathematical model of the hepatitis E virus using the fractional Atangana-Baleanu (AB) derivative. The existence and uniqueness of the solution obtained for the proposed model are presented with the help of the fixed-point hypothesis. The Adams-Bashforth technique is employed to analyse and find the solution for the future model, and the numerical simulations have been conducted in order to validate the efficiency of the Atangana-Baleanu derivative. The present investigation shows that the dynamics of the hepatitis E virus model noticeably depends on the time instant as well as the time history, which can be efficiently modelled by employing the theory of fractional calculus.

53 citations


Journal ArticleDOI
14 Mar 2019
TL;DR: In this article, the q-homotopy analysis transform method (q-HATM) is employed to find the solution for the fractional Kolmogorov-Petrovskii-Piskunov (FKPP) equation in the present frame work.
Abstract: The q -homotopy analysis transform method ( q -HATM) is employed to find the solution for the fractional Kolmogorov–Petrovskii–Piskunov (FKPP) equation in the present frame work. To ensure the applicability and efficiency of the proposed algorithm, we consider three distinct initial conditions with two of them having Jacobi elliptic functions. The numerical simulations have been conducted to verify that the proposed scheme is reliable and accurate. Moreover, the uniqueness and convergence analysis for the projected problem is also presented. The obtained results elucidate that the proposed technique is easy to implement and very effective to analyze the complex problems arising in science and technology.

52 citations


Journal ArticleDOI
TL;DR: In this paper, the approximated analytical solutions for nonlinear dispersive fractional Zakharov-Kuznetsov (FZK(a, b, c)) equations are obtained with the help of two novel techniques, called fractional natural decomposition method (FNDM) and q-homotopy analysis transform method (q-HATM).

52 citations




Journal ArticleDOI
01 Jul 2019-Pramana
TL;DR: In this article, a solution of coupled fractional Navier-Stokes equation is computed numerically using the proposed q-homotopy analysis transform method (q-HATM), and the solution is found in fast convergent series.
Abstract: In this paper, a solution of coupled fractional Navier–Stokes equation is computed numerically using the proposed q-homotopy analysis transform method (q-HATM), and the solution is found in fast convergent series. The given test examples illustrate the leverage and effectiveness of the proposed technique. The obtained results are demonstrated graphically. The present method handles the series solution in a large admissible domain in an extreme manner. It offers us a modest way to adjust the convergence region of the solution. Results with graphs explicitly reveal the efficiency and capability of the proposed algorithm.

Journal ArticleDOI
07 Mar 2019
TL;DR: In this paper, a non-linear fractional order Swift-Hohenberg equation in the presence and absence of dispersive terms is considered and the effect of bifurcation and dispersive parameters with physical importance on the probability density function for distinct fractional Brownian and standard motions are studied.
Abstract: In this paper, the approximated analytical solution for the fractional Swift–Hohenberg (S–H) equation has been investigated with the help of the residual power series method (RPSM). To ensure the applicability and efficiency of the proposed technique, we consider a non-linear fractional order Swift–Hohenberg equation in the presence and absence of dispersive terms. The effect of bifurcation and dispersive parameters with physical importance on the probability density function for distinct fractional Brownian and standard motions are studied and presented through plots. The results obtained show that the proposed technique is simple to implement and very effective for analyzing the complex problems that arise in connected areas of science and technology.

Journal ArticleDOI
TL;DR: In this paper, numerical solution of fractional order Navier-Stokes equations in unsteady viscous fluid flow is found using q-homotopy analysis transform scheme.
Abstract: Abstract In this paper, numerical solution of fractional order Navier-Stokes equations in unsteady viscous fluid flow is found using q-homotopy analysis transform scheme. Fractional derivative is considered in Caputo sense. The proposed technique is a blend of q-homotopy analysis scheme and transform of Laplace. It executes well in efficiency and provides h-curves that show convergence range of series solution.

Journal ArticleDOI
TL;DR: In this article, the authors proposed a solution for fractional Richards equation describing the water transport in unsaturated porous media using q-homotopy analysis transform method (q-HATM).
Abstract: In this paper, we find the solution for fractional Richards equation describing the water transport in unsaturated porous media using q-homotopy analysis transform method (q-HATM).The proposed technique is graceful amalgamations of Laplace transform technique with q-homotopy analysis scheme, and fractional derivative defined with Atangana-Baleanu (AB) operator. The fixed point hypothesis considered in order to demonstrate the existence and uniqueness of the obtained solution for the proposed fractional order model. In order to validate and illustrate the efficiency of the future technique, we analysed the projected model in terms of fractional order. Meanwhile, the physical behaviour of the q-HATM solutions have been captured in terms of plots for diverse fractional order and the numerical simulation is also demonstrated. The achieved results illuminate that, the future algorithm is easy to implement, highly methodical as well as effective and very accurate to analyse the behaviour of nonlinear differential equations of fractional order arisen in the connected areas of science and engineering.

Journal ArticleDOI
TL;DR: In this article, an efficient technique is employed to study the modified Boussinesq and approximate long wave equations of the Caputo fractional time derivative, namely the q-homotopy analysis transform method.
Abstract: In this paper, an efficient technique is employed to study the modified Boussinesq and approximate long wave equations of the Caputo fractional time derivative, namely the q-homotopy analysis transform method. These equations play a vital role in describing the properties of shallow water waves through distinct dispersion relation. The convergence analysis and error analysis are presented in the present investigation for the future scheme. We illustrate two examples to demonstrate the leverage and effectiveness of the proposed scheme, and the error analysis is discussed to verify the accuracy. The numerical simulation is conducted to ensure the exactness of the future technique. The obtained numerical and graphical results are presented, the proposed scheme is computationally very accurate and straightforward to study and find the solution for fractional coupled nonlinear complex phenomena arising in science and technology.

Journal ArticleDOI
TL;DR: The proposed algorithm is an elegant mixture of homotopy analysis technique with Laplace transform, which is computationally very effective and more accurate to analyse fractional nonlinear coupled Burgers differential equations.

Journal ArticleDOI
TL;DR: In this article, the numerical solution of time-fractional Jaulent-Miodek (JM) equations with the aid of two novel techniques namely, coupled fractional reduced differential transfor...
Abstract: In present work, we investigate the numerical solution of time-fractional Jaulent–Miodek (JM) equations with the aid of two novel techniques namely, coupled fractional reduced differential transfor...

Journal ArticleDOI
01 Nov 2019-Pramana
TL;DR: In this paper, the q-homotopy analysis transform method (q-HATM) is applied to find approximated analytical solution for the system of fractional differential equations describing the unsteady flow of a polytropic gas.
Abstract: In the present investigation, the q-homotopy analysis transform method (q-HATM) is applied to find approximated analytical solution for the system of fractional differential equations describing the unsteady flow of a polytropic gas. Numerical simulation has been conducted to prove that the proposed technique is reliable and accurate, and the outcomes are revealed using plots and tables. The comparison between the obtained solutions and the exact solutions shows that the proposed method is efficient and effective in solving nonlinear complex problems. Moreover, the proposed algorithm controls and manipulates the obtained series solution in a huge acceptable region in an extreme manner and it provides us a simple procedure to control and adjust the convergence region of the series solution.

Journal ArticleDOI
01 Nov 2019
TL;DR: In this article, it was shown that if the Ricci tensor of a manifold is a Ricci soliton on a manifold M, then M is either a homothetic to an Einstein manifold or vanishes.
Abstract: In this paper we study a special type of metric called $$*$$ -Ricci soliton on para-Sasakian manifold. We prove that if the para-Sasakian metric is a $$*$$ -Ricci soliton on a manifold M, then M is either $$\mathcal {D}$$ -homothetic to an Einstein manifold, or the Ricci tensor of M with respect to the canonical paracontact connection vanishes.

Book ChapterDOI
20 Apr 2019
TL;DR: In this article, the authors proposed a homotopy analysis transform method (HATM) for the time-fractional coupled WBK equations describing the propagation of shallow water waves.
Abstract: In the present work, the approximated analytical solution for the time-fractional coupled Whitham-Broer-Kaup (WBK) equations describing the propagation of shallow water waves are obtained with the aid of an efficient computational technique called, \( q \)-Homotopy analysis transform method (briefly, \( q \)-HATM). To demonstrate the reliability and efficiency of the proposed technique, two examples are illustrated. The homotopy polynomials are hired in order to handle the nonlinear terms and the suggested algorithm provides the auxiliary parameters \( \hbar \) and \( \fancyscript{n} \), which help us to control and adjust the convergence region of the obtained series solution. Numerical simulation has been carried out in terms of absolute error. The obtained results revels that, the proposed algorithm is highly methodical and very efficient to solve coupled nonlinear differential system.


Journal ArticleDOI
TL;DR: In this paper, the Fischer-Marsden conjecture on almost Kenmotsu manifolds was studied and the authors characterized non-kappa, \mu, \mu )^\prime -almost-kempe manifolds satisfying the Fischer−Marsden equation.
Abstract: The purpose of this paper is to study the Fischer–Marsden conjecture on a class of almost Kenmotsu manifolds. We characterize non-Kenmotsu $$(\kappa , \mu )^\prime $$ -almost Kenmotsu manifolds satisfying the Fischer–Marsden equation.

Book ChapterDOI
07 Nov 2019
TL;DR: In this article, an efficient technique called, ''q \)-homotopy analysis transform method (\( q \)-HATM) in order to find the solution for the model of thrombin receptor activation mechanism (TRAM) and examine the nature of solution with distinct fractional order.
Abstract: In the present work, we haired an efficient technique called, \( q \)-homotopy analysis transform method (\( q \)-HATM) in order to find the solution for the model of thrombin receptor activation mechanism (TRAM) and examine the nature of \( q \)-HATM solution with distinct fractional order. The considered model elucidates the TRA mechanism in calcium signalling, and this mechanism plays a vital role in the human body. We defined fractional derivative defined with Atangana-Baleanu (AB) operator and the projected scheme is an amalgamation of Laplace transform with \( q \)-homotopy analysis scheme. For the achieved results, to present the existence and uniqueness we hired the fixed point hypothesis. To validate and illustrate the effectiveness of the considered scheme, we examined the projected model with arbitrary order. The behaviour of the achieved results is captured in terms of plots and also showed the importance of the parameters offered by the considered solution procedure. The attained results illuminate, the projected scheme is easy to employ and more effective in order to analyse the behaviour of fractional order differential systems exemplifying real word problems associated with science and technology.

Posted Content
TL;DR: In this paper, the authors study $(\epsilon)$-para-Sasakian 3-manifolds satisfying certain conditions on the $\mathcal{Z}$ tensor.
Abstract: The object of this paper is study $(\epsilon)$-para-Sasakian 3-manifolds satisfying certain conditions on the $\mathcal{Z}$ tensor. We characterize, $\mathcal{Z}$-symmetric; $\mathcal{Z}$-semisymmetric; $\mathcal{Z}$-pseudosymmetric; and projectively $\mathcal{Z}$-semisymmetric conditions on an $(\epsilon)$-para-Sasakian 3-manifold.