Browsing by Author "Kumar, Devendra"

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Citation Count: Kumar, D., Singh, J., Baleanu, D. (2017). A fractional model of convective radial fins with temperature-dependent thermal conductivity. Romanian Reports In Physics, 69(1).
A fractional model of convective radial fins with temperature-dependent thermal conductivity
(Editura Acad Romane, 2017) Kumar, Devendra; Singh, Jagdev; Baleanu, Dumitru
The principal purpose of the present article is to examine a fractional model of convective radial fins having constant and temperature-dependent thermal conductivity. In order to solve fractional order energy balance equation, a numerical algorithm namely homotopy analysis transform method is considered. The fin temperature is derived in terms of thermo-geometric fin parameter. Our method is not limited to the use of a small parameter, such as in the standard perturbation technique. The numerical simulation for temperature and fin tip temperature are presented graphically. The results can be used in thermal design to consider radial fins having both constant and temperature-dependent thermal conductivity.
Citation Count: Taneja, Komal...et al. (2023). "A Higher-Order Approach For Time-Fractional Generalized Burgers' Equation", Fractals-Complex Geometry Patterns And Scaling In Nature And Society, Vol.31, No.07
A Higher-Order Approach For Time-Fractional Generalized Burgers' Equation
(2023) Taneja, Komal; Deswal, Komal; Kumar, Devendra; Baleanu, Dumitru; 56389
A fast higher-order scheme is established for solving inhomogeneous time-fractional generalized Burgers' equation. The time-fractional operator is taken as the modified operator with the Mittag-Leffler kernel. Through stability analysis, it has been demonstrated that the proposed numerical approach is unconditionally stable. The convergence of the numerical method is analyzed theoretically using von Neumann's method. It has been proved that the proposed numerical method is fourth-order convergent in space and second-order convergent in time in the L-2-norm. The scheme's proficiency and effectiveness are examined through two numerical experiments to validate the theoretical estimates. The tabular and graphical representations of numerical results confirm the high accuracy and versatility of the scheme.
Citation Count: Sushila...at all (2021). "A hybrid analytical algorithm for thin film flow problem occurring in non-Newtonian fluid mechanics", Ain Shams Engineering Journal, Vol. 12, No. 2, pp. 2297-2302.
A hybrid analytical algorithm for thin film flow problem occurring in non-Newtonian fluid mechanics
(2021) Sushila; Singh, Jagdev; Kumar, Devendra; Baleanu, Dumitru; 56389
In this work, we investigate thin film flow of a third grade fluid down a inclined plane. The solution of a nonlinear boundary value problem (BVP) is derived by using an effective well organized computational scheme namely homotopy perturbation Elzaki transform method. Furthermore, this model is also resolved by Elzaki decomposition technique. The outcomes achieved by these two approaches are consistent with each other and because of that this technique may be regarded as an optional and effective scheme for determining results of linear and nonlinear BVP. Moreover, the homotopy perturbation Elzaki transform method leads over the Elzaki decomposition method since the nonlinear problems are solved without utilization of Adomian polynomials. (C) 2020 The Authors. Published by Elsevier B.V. on behalf of Faculty of Engineering, Ain Shams University.
Citation Count: Kumar, D., Singh J., Baleanu, D. (2017). A hybrid computational approach for Klein-Gordon equations on Cantor sets. Nonlinear Dynamics, 87(1), 511-517. http://dx.doi.org/ 10.1007/s11071-016-3057-x
A hybrid computational approach for Klein-Gordon equations on Cantor sets
(Springer, 2017) Kumar, Devendra; Singh, Jagdev; Baleanu, Dumitru
In this letter, we present a hybrid computational approach established on local fractional Sumudu transform method and homotopy perturbation technique to procure the solution of the Klein-Gordon equations on Cantor sets. Four examples are provided to show the accuracy and coherence of the proposed technique. The outcomes disclose that the present computational approach is very user friendly and efficient to compute the nondifferentiable solution of Klein-Gordon equation involving local fractional operator.
Citation Count: Kumar, Devendra; Singh, Jagdev; Baleanu, Dumitru, "A new analysis for fractional model of regularized long-wave equation arising in ion acoustic plasma waves", Mathematical Methods In The Applied Sciences, Vol.40, No.15, pp.5642-5653, (2017).
A new analysis for fractional model of regularized long-wave equation arising in ion acoustic plasma waves
(2017) Kumar, Devendra; Singh, Jagdev; Baleanu, Dumitru; 56389
The key purpose of the present work is to constitute a numerical scheme based on q-homotopy analysis transform method to examine the fractional model of regularized long-wave equation. The regularized long-wave equation explains the shallow water waves and ion acoustic waves in plasma. The proposed technique is a mixture of q-homotopy analysis method, Laplace transform, and homotopy polynomials. The convergence analysis of the suggested scheme is verified. The scheme provides and n-curves, which show that the range convergence of series solution is not a local point effects and elucidate that it is superior to homotopy analysis method and other analytical approaches.
Citation Count: Singh, J., Kumar, D., Baleanu, Dumitru, "A New Analysis of Fractional Fish Farm Model Associated With Mittag-Leffler-Type Kernel", International Journal of Biomathematics, Vol. 13, No. 2, (2020).
A New Analysis of Fractional Fish Farm Model Associated With Mittag-Leffler-Type Kernel
(World Scientific Publ CO PTE LTD, 2020) Singh, Jagdev; Kumar, Devendra; Baleanu, Dumitru; 56389
In this paper, we analyze the dynamical behavior of fish farm model related to Atangana-Baleanu derivative of arbitrary order. The model is constituted with the group of nonlinear differential equations having nutrients, fish and mussel. We have included discrete kind gestational delay of fish. The solution of fish farm model is determined by employing homotopy analysis transforms method (HATM). Existence of and uniqueness of solution are studied through Picard-Lindelof approach. The influence of order of new non-integer order derivative on nutrients, fish and mussel is discussed. The complete study reveals that the outer food supplies manage the behavior of the model. Moreover, to show the outcomes of the study, some numerical results are demonstrated through graphs. © 2020 World Scientific Publishing Company.
Citation Count: Kumar, Devendra; Singh, Jagdev; Baleanu, Dumitru, "A new analysis of the Fornberg-Whitham equation pertaining to a fractional derivative with Mittag-Leffler-type kernel", European Physical Journal Plus, Vol. 133, No. 2, (2018)
A New Analysis of the Fornberg-Whitham Equation Pertaining to A Fractional Derivative With Mittag-Leffler-Type Kernel
(Springer Heidelberg, 2018) Kumar, Devendra; Singh, Jagdev; Baleanu, Dumitru; 56389
The mathematical model of breaking of non-linear dispersive water waves with memory effect is very important in mathematical physics. In the present article, we examine a novel fractional extension of the non-linear Fornberg-Whitham equation occurring in wave breaking. We consider the most recent theory of differentiation involving the non-singular kernel based on the extended Mittag-Leffler-type function to modify the Fornberg-Whitham equation. We examine the existence of the solution of the non-linear Fornberg-Whitham equation of fractional order. Further, we show the uniqueness of the solution. We obtain the numerical solution of the new arbitrary order model of the non-linear Fornberg-Whitham equation with the aid of the Laplace decomposition technique. The numerical outcomes are displayed in the form of graphs and tables. The results indicate that the Laplace decomposition algorithm is a very user-friendly and reliable scheme for handling such type of non-linear problems of fractional order.
Citation Count: Kumar, Devendra...et al. (2019). "A new fractional exothermic reactions model having constant heat source in porous media with power, exponential and Mittag-Leffler laws", International Journal of Heat and Mass Transfer, Vol. 138, pp. 1222-1227.
A new fractional exothermic reactions model having constant heat source in porous media with power, exponential and Mittag-Leffler laws
(Pergamon-Elsevier Science LTD, 2019) Kumar, Devendra; Singh, Jagdev; Tanwar, Kumud; Baleanu, Dumitru; 56389
The present article deals with the exothermic reactions model having constant heat source in the porous media with strong memory effects. The Caputo, Caputo-Fabrizio and Atangana-Baleanu fractional operators are used to induce memory effects in the mathematical modeling of exothermic reactions. The patterns of heat flow profiles are very essential for heat transfer in every kind of the thermal insulation. In the present investigation, we focus on the driving force problem due to the fact that temperature gradient is assumed. The mathematical equation of the problem is confined in a fractional energy balance equation (FEBE), which furnishes the temperature portrayal in conduction state having uniform heat source on steady state. The fractional Laplace decomposition technique is utilized to obtain the numerical solution of the corresponding FEBE describing the exothermic reactions. Some numerical results for the fractional exothermic reactions model are presented through graphs and tables. (C) 2019 Elsevier Ltd. All rights reserved.
Citation Count: Kumar, Devendra; Singh, Jagdev; Baleanu, Dumitru, "A New Fractional Model For Convective Straight Fins With Temperature-Dependent Thermal Conductivity", Thermal Science, Vol. 22, No: 6, pp. 2791-2802, (2018).
A New Fractional Model For Convective Straight Fins With Temperature-Dependent Thermal Conductivity
(Vinca Inst Nuclear Sci, 2018) Kumar, Devendra; Singh, Jagdev; Baleanu, Dumitru; 56389
The key aim of this work is to present a new non-integer model for convective straight fins with temperature-dependent thermal conductivity associated with Caputo-Fabrizio fractional derivative. The fractional energy balance equation is solved by using homotopy perturbation method coupled with Laplace transform method. The efficiency of straight fin has been derived in terms of thermo-geometric fin parameter. The numerical results derived by the application of suggested scheme are demonstrated graphically. The subsequent correlation equations are very helpful for thermal design scientists and engineers to design straight fins having temperature-dependent thermal conductivity.
Citation Count: Singh, Jagdev...et al. (2017). A new fractional model for giving up smoking dynamics, Advances in Difference Equations.
A new fractional model for giving up smoking dynamics
(Springer Open, 2017) Singh, Jagdev; Kumar, Devendra; Al Qurashi, Maysaa Mohamed; Baleanu, Dumitru; 56389
The key purpose of the present work is to examine a fractional giving up smoking model pertaining to a new fractional derivative with non-singular kernel. The numerical simulations are conducted with the aid of an iterative technique. The existence of the solution is discussed by employing the fixed point postulate, and the uniqueness of the solution is also proved. The effect of various parameters is shown graphically. The numerical results for the smoking model associated with the new fractional derivative are compared with numerical results for a smoking model pertaining to the standard derivative and Caputo fractional derivative.
Citation Count: Kumar, Devendra...et al. (2019). "A new fractional SIRS-SI malaria disease model with application of vaccines, antimalarial drugs, and spraying", Advances in Difference Equations.
A new fractional SIRS-SI malaria disease model with application of vaccines, antimalarial drugs, and spraying
(Springer Open, 2019) Kumar, Devendra; Singh, Jagdev; Al Qurashi, Maysaa Mohamed; Baleanu, Dumitru; 56389
The present paper deals with a new fractional SIRS-SI model describing the transmission of malaria disease. The SIRS-SI malaria model is modified by using the Caputo-Fabrizio fractional operator for the inclusion of memory. We also suggest the utilization of vaccines, antimalarial medicines, and spraying for the treatment and control of the malaria disease. The theory of fixed point is utilized to examine the existence of the solution of a fractional SIRS-SI model describing spreading of malaria. The uniqueness of the solution of SIRS-SI model for malaria is also analyzed. It is shown that the treatments have great impact on the dynamical system of human and mosquito populations. The numerical simulation of fractional SIRS-SI malaria model is performed with the aid of HATM and Maple packages to show the effect of different parameters of the treatment of malaria disease. The numerical results for fractional SIRS-SI malaria model reveal that the recommended approach is very accurate and effective.
Citation Count: Baleanu, Dumitru; Kumar, Devendra; Singh, Jagdev,, "A New Numerical Algorithm For Fractional Fitzhugh-Nagumo Equation Arising in Transmission of Nerve Impulses", Nonlinear Dynamics, 91, No. 1, pp. 307-317, (2018).
A New Numerical Algorithm For Fractional Fitzhugh-Nagumo Equation Arising in Transmission of Nerve Impulses
(Springer, 2018) Kumar, Devendra; Singh, Jagdev; Baleanu, Dumitru; 56389
The principal objective of this study is to present a new numerical scheme based on a combination of q-homotopy analysis approach and Laplace transform approach to examine the Fitzhugh-Nagumo (F-N) equation of fractional order. The F-N equation describes the transmission of nerve impulses. In order to handle the nonlinear terms, the homotopy polynomials are employed. To validate the results derived by employing the used scheme, we study the F-N equation of arbitrary order by using the fractional reduced differential transform scheme. The error analysis of the proposed approach is also discussed. The outcomes are shown through the graphs and tables that elucidate that the used schemes are very fantastic and accurate.
Citation Count: Chawla, Reetika;...et.al. (2022). "A novel finite difference based numerical approach for Modified Atangana-Baleanu Caputo derivative", AIMS Mathematics, Vol.7, No.9, pp.17252-17268.
A novel finite difference based numerical approach for Modified Atangana-Baleanu Caputo derivative
(2022) Chawla, Reetika; Deswal, Komal; Kumar, Devendra; Baleanu, Dumitru; 56389
In this paper, a new approach is presented to investigate the time-fractional advection-dispersion equation that is extensively used to study transport processes. The present modified fractional derivative operator based on Atangana Baleanu’s definition of a derivative in the Caputo sense involves singular and non-local kernels. A numerical approximation of this new modified fractional operator is provided and applied to an advection-dispersion equation. Through Fourier analysis it has been proved that the proposed scheme is unconditionally stable. Numerical examples are solved that validate the theoretical results presented in this paper and ensure the proficiency of the numerical scheme.
Citation Count: Hristov, Jordan; Kumar, Devendra; Baleanu, Dumitru (2021). "ADVANCED MODELLING OF TRANSPORT PROBLEMS IN HEAT-MASS AND RELATED FLUID MECHANICS", THERMAL SCIENCE, Vol. 25, No. SI, pp. SXI-SXI.
ADVANCED MODELLING OF TRANSPORT PROBLEMS IN HEAT-MASS AND RELATED FLUID MECHANICS
(2021) Hristov, Jordan; Kumar, Devendra; Baleanu, Dumitru; 56389
Citation Count: Pandey, Amit K.;...et.al. (2022). "An efficient algorithm for the numerical evaluation of pseudo differential operator with error estimation", AIMS Mathematics, Vol.7, No.10, pp.17829-17842.
An efficient algorithm for the numerical evaluation of pseudo differential operator with error estimation
(2022) Pandey, Amit K.; Tripathi, Manoj P.; Singh, Harendra; Rao, Pentyala S.; Kumar, Devendra; Baleanu, D.; 56389
In this paper we introduce an efficient and new numerical algorithm for evaluating a pseudo differential operator. The proposed algorithm is time saving and fruitful. The theoretical as well as numerical error estimation of the algorithm is established, together with its stability analysis. We have provided numerical illustrations and established that the numerical findings echo the analytical findings. The proposed technique has a convergence rate of order three. CPU time of computation is also listed. Trueness of numerical findings are validated using figures.
Citation Count: Singh, Jagdev...et al. (2021). "An efficient computational approach for local fractional Poisson equation in fractal media", Numerical Methods for Partial Differential Equations, Vol. 37, No. 2, pp. 1439-1448.
An efficient computational approach for local fractional Poisson equation in fractal media
(2021) Singh, Jagdev; Ahmadian, Ali; Rathore, Sushila; Kumar, Devendra; Baleanu, Dumitru; Salimi, Mehdi; Salahshour, Soheil; 56389
In this article, we analyze local fractional Poisson equation (LFPE) by employing q-homotopy analysis transform method (q-HATM). The PE describes the potential field due to a given charge with the potential field known, one can then calculate gravitational or electrostatic field in fractal domain. It is an elliptic partial differential equations (PDE) that regularly appear in the modeling of the electromagnetic mechanism. In this work, PE is studied in the local fractional operator sense. To handle the LFPE some illustrative example is discussed. The required results are presented to demonstrate the simple and well-organized nature of q-HATM to handle PDE having fractional derivative in local fractional operator sense. The results derived by the discussed technique reveal that the suggested scheme is easy to employ and computationally very accurate. The graphical representation of solution of LFPE yields interesting and better physical consequences of Poisson equation with local fractional derivative.
Citation Count: Kumar, Devendra...et al. (2018). "An Efficient Computational Technique for Fractal Vehicular Traffic Flow", Entropy, Vol. 20, No.4.
An Efficient Computational Technique for Fractal Vehicular Traffic Flow
(MDPI, 2018) Kumar, Devendra; Tchier, Fairouz; Singh, Jagdev; Baleanu, Dumitru; 56389
In this work, we examine a fractal vehicular traffic flow problem. The partial differential equations describing a fractal vehicular traffic flow are solved with the aid of the local fractional homotopy perturbation Sumudu transform scheme and the local fractional reduced differential transform method. Some illustrative examples are taken to describe the success of the suggested techniques. The results derived with the aid of the suggested schemes reveal that the present schemes are very efficient for obtaining the non-differentiable solution to fractal vehicular traffic flow problem.
Citation Count: Veeresha, P...et al. (2020). "An Efficient Computational Technique for Fractional Model of Generalized Hirota-Satsuma-Coupled Korteweg-de Vries and Coupled Modified Korteweg-de Vries Equations", Journal of Computational and Nonlinear Dynamics, Vol. 15, No. 7.
An Efficient Computational Technique for Fractional Model of Generalized Hirota-Satsuma-Coupled Korteweg-de Vries and Coupled Modified Korteweg-de Vries Equations
(2020) Veeresha, P.; Prakasha, D. G.; Kumar, Devendra; Baleanu, Dumitru; Singh, Jagdev; 56389
The aim of the present investigation to find the solution for fractional generalized Hirota-Satsuma coupled Korteweg-de-Vries (KdV) and coupled modified KdV (mKdV) equations with the aid of an efficient computational scheme, namely, fractional natural decomposition method (FNDM). The considered fractional models play an important role in studying the propagation of shallow-water waves. Two distinct initial conditions are choosing for each equation to validate and demonstrate the effectiveness of the suggested technique. The simulation in terms of numeric has been demonstrated to assure the proficiency and reliability of the future method. Further, the nature of the solution is captured for different value of the fractional order. The comparison study has been performed to verify the accuracy of the future algo
Citation Count: Singh, Jagdev...et al. (2018). "An efficient numerical algorithm for the fractional Drinfeld-Sokolov-Wilson equation", Applied Mathematics and Computation, Vol. 335, pp. 12-24.
An efficient numerical algorithm for the fractional Drinfeld-Sokolov-Wilson equation
(Elsevier Science INC, 2018) Singh, Jagdev; Kumar, Devendra; Baleanu, Dumitru; Rathore, Sushila; 56389
The fundamental purpose of the present paper is to apply an effective numerical algorithm based on the mixture of homotopy analysis technique, Sumudu transform approach and homotopy polynomials to obtain the approximate solution of a nonlinear fractional Drinfeld-Sokolov-Wilson equation. The nonlinear Drinfeld-Sokolov-Wilson equation naturally occurs in dispersive water waves. The uniqueness and convergence analysis are shown for the suggested technique. The convergence of the solution is fixed and managed by auxiliary parameter h. The numerical results are shown graphically. Results obtained by the application of the technique disclose that the suggested scheme is very accurate, flexible, effective and simple to use. (C) 2018 Elsevier Inc. All rights reserved.
Citation Count: Kumar, Sunil...et al. (2020). "An Efficient Numerical Method for Fractional SIR Epidemic Model of Infectious Disease by Using Bernstein Wavelets", Mathematics, Vol. 8, No. 4.
An Efficient Numerical Method for Fractional SIR Epidemic Model of Infectious Disease by Using Bernstein Wavelets
(2020) Kumar, Sunil; Ahmadian, Ali; Kumar, Ranbir; Kumar, Devendra; Singh, Jagdev; Baleanu, Dumitru; Salimi, Mehdi; 56389
In this paper, the operational matrix based on Bernstein wavelets is presented for solving fractional SIR model with unknown parameters. The SIR model is a system of differential equations that arises in medical science to study epidemiology and medical care for the injured. Operational matrices merged with the collocation method are used to convert fractional-order problems into algebraic equations. The Adams-Bashforth-Moulton predictor correcter scheme is also discussed for solving the same. We have compared the solutions with the Adams-Bashforth predictor correcter scheme for the accuracy and applicability of the Bernstein wavelet method. The convergence analysis of the Bernstein wavelet has been also discussed for the validity of the method.