Matematik Bölümü Yayın Koleksiyonu

Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/413

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Author: search.filters.author.Kumar, DevendraPublisher: search.filters.publisher.Amer inst Mathematical Sciences-aims

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  • Article
    Citation - WoS: 22
    Citation - Scopus: 25
    New Approach on Controllability of Hilfer Fractional Derivatives With Nondense Domain
    (Amer inst Mathematical Sciences-aims, 2022) Jothimani, Kasthurisamy; Ravichandran, Chokkalingam; Baleanu, Dumitru; Kumar, Devendra; Nisar, Kottakkaran Sooppy
    This work picturizes the results on the controllability of the nondense Hilfer neutral fractional derivative (HNFD). The uniqueness and controllability of HNFD are discussed with Winch theorem and Banach contraction technique. In addition, a numerical approximation is given to deal with different criteria of our results.
  • Article
    An Efficient Algorithm for the Numerical Evaluation of Pseudo Differential Operator With Error Estimation
    (Amer inst Mathematical Sciences-aims, 2022) Pandey, Amit K.; Tripathi, Manoj P.; Singh, Harendra; Rao, Pentyala S.; Kumar, Devendra; Baleanu, D.
    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.
  • Article
    Citation - WoS: 20
    A Novel Finite Difference Based Numerical Approach for Modified Atangana-Baleanu Caputo Derivative
    (Amer inst Mathematical Sciences-aims, 2022) Deswal, Komal; Kumar, Devendra; Baleanu, Dumitru; Chawla, Reetika
    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.