Scopus İndeksli Yayınlar Koleksiyonu

Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651

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Author: search.filters.author.Kumar, DevendraPublisher: search.filters.publisher.Springer

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Now showing 1 - 7 of 7
  • Article
    Citation - WoS: 10
    Citation - Scopus: 18
    Identifying the Space Source Term Problem for Time-Space Diffusion Equation
    (Springer, 2020) Karapinar, Erdal; Kumar, Devendra; Sakthivel, Rathinasamy; Nguyen Hoang Luc; Can, N. H.; Luc, Nguyen Hoang
    In this paper, we consider an inverse source problem for the time-space-fractional diffusion equation. Here, in the sense of Hadamard, we prove that the problem is severely ill-posed. By applying the quasi-reversibility regularization method, we propose by this method to solve the problem (1.1). After that, we give an error estimate between the sought solution and regularized solution under a prior parameter choice rule and a posterior parameter choice rule, respectively. Finally, we present a numerical example to find that the proposed method works well.
  • Article
    An Q-Uniformly Convergent Technique for Singularly Perturbed Problems, With an Interior Turning Point Occurring in Chemical Processes
    (Springer, 2025) Kumari, Parvin; Kumar, Devendra; Baleanu, Dumitru
    A parameter-uniform solution is presented for singularly perturbed turning point problems with twin boundary layers. A fitted mesh is created in order to resolve the layers, and the provided equation is discretized using the cubic B-spline basis functions on this mesh. For the analytic solution and its derivatives, asymptotic bounds are provided. A brief analysis shows that the method is first-order precise in time and second-order accurate (up to a logarithm factor) in space, and that it is uniformly convergent regardless of the minuscule parameter. Two test problems are offered in order to verify the theoretical results.
  • Article
    Citation - WoS: 6
    Citation - Scopus: 4
    Novel Numerical Approach for Time Fractional Equations With Nonlocal Condition
    (Springer, 2024) Deswal, Komal; Kumar, Devendra; Baleanu, Dumitru; Taneja, Komal
    A numerical method for solving inhomogeneous nonlocal time fractional convection-diffusion-reaction equations with variable coefficients has been developed. The fractional time operator is taken in the sense of the modified operator with the Mittag-Leffler kernel. The numerical method is based on the modified Gauss elimination with Taylor's expansion. Through rigorous analysis, it has been proved that the given method is unconditionally stable and second-order convergent in space and time. The numerical results for three test problems illustrate the efficiency and validity of the theoretical estimates.
  • Article
    Citation - WoS: 122
    Citation - Scopus: 138
    A New Numerical Algorithm for Fractional Fitzhugh-Nagumo Equation Arising in Transmission of Nerve Impulses
    (Springer, 2018) Singh, Jagdev; Baleanu, Dumitru; Kumar, Devendra
    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.
  • Article
    Citation - WoS: 158
    Citation - Scopus: 150
    A New Fractional Sirs-Si Malaria Disease Model With Application of Vaccines, Antimalarial Drugs, and Spraying
    (Springer, 2019) Singh, Jagdev; Al Qurashi, Maysaa; Baleanu, Dumitru; Kumar, Devendra
    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.
  • Article
    Citation - WoS: 121
    Citation - Scopus: 142
    On the Analysis of Fractional Diabetes Model With Exponential Law
    (Springer, 2018) Kumar, Devendra; Baleanu, Dumitru; Singh, Jagdev
    In this work, we study the diabetes model and its complications with the Caputo-Fabrizio fractional derivative. A deterministic mathematical model pertaining to the fractional derivative of the diabetes mellitus is discussed. The analytical solution of the diabetes model is derived by exerting the homotopy analysis method, the Laplace transform and the Pade approximation. Moreover, existence and uniqueness of the solution are examined by making use of fixed point theory and the Picard-Lindelof approach. Ultimately, for illustrating the obtained results some numerical simulations are performed.
  • Article
    Citation - WoS: 119
    Citation - Scopus: 130
    A Hybrid Computational Approach for Klein-Gordon Equations on Cantor Sets
    (Springer, 2017) Singh, Jagdev; Baleanu, Dumitru; Kumar, Devendra
    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.