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, Devendra

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Now showing 1 - 10 of 45
  • Article
    Citation - WoS: 63
    Citation - Scopus: 76
    A Fractional Model of Convective Radial Fins With Temperature-Dependent Thermal Conductivity
    (Editura Acad Romane, 2017) Kumar, Devendra; Baleanu, Dumitru; Singh, Jagdev; Baleanu, Dumitru; Matematik
    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.
  • Article
    Citation - WoS: 9
    Analytic Study of Allen-Cahn Equation of Fractional Order
    (int Center Scientific Research & Studies, 2017) Kumar, Devendra; Baleanu, Dumitru; Singh, Jagdev; Baleanu, Dumitru; Matematik
    The key purpose of the present article is to analyze the Allen Cahn equation of fractional order. The fractional Allen-Cahn equation models the process of phase separation in iron alloys, along with order-disorder transitions. The analytical technique is employed to investigate the fractional model of Allen-Cahn equation. The numerical results are shown graphically. The outcomes show that the analytical technique is very efficient and user friendly for handling nonlinear fractional differential equations describing the real world problems.
  • Editorial
    Advanced Modelling of Transport Problems in Heat-Mass and Related Fluid Mechanics
    (Vinca inst Nuclear Sci, 2021) Hristov, Jordan; Baleanu, Dumitru; Kumar, Devendra; Baleanu, Dumitru; Matematik
  • Editorial
  • 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
    Citation - WoS: 12
    Citation - Scopus: 21
    Generalized Invexity and Duality in Multiobjective Variational Problems Involving Non-Singular Fractional Derivative
    (de Gruyter Poland Sp Z O O, 2022) Kumar, Devendra; Alshehri, Hashim M.; Singh, Jagdev; Baleanu, Dumitru; Dubey, Ved Prakash
    In this article, we extend the generalized invexity and duality results for multiobjective variational problems with fractional derivative pertaining to an exponential kernel by using the concept of weak minima. Multiobjective variational problems find their applications in economic planning, flight control design, industrial process control, control of space structures, control of production and inventory, advertising investment, impulsive control problems, mechanics, and several other engineering and scientific problems. The proposed work considers the newly derived Caputo-Fabrizio (CF) fractional derivative operator. It is actually a convolution of the exponential function and the first-order derivative. The significant characteristic of this fractional derivative operator is that it provides a non-singular exponential kernel, which describes the dynamics of a system in a better way. Moreover, the proposed work also presents various weak, strong, and converse duality theorems under the diverse generalized invexity conditions in view of the CF fractional derivative operator.
  • 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.
  • Article
    Citation - WoS: 8
    Citation - Scopus: 9
    Numerical Simulation for Generalized Time-Fractional Burgers' Equation With Three Distinct Linearization Schemes
    (Asme, 2023) Deswal, Komal; Kumar, Devendra; Baleanu, Dumitru; Chawla, Reetika; Reetika, Chawla
    In the present study, we examined the effectiveness of three linearization approaches for solving the time-fractional generalized Burgers' equation using a modified version of the fractional derivative by adopting the Atangana-Baleanu Caputo derivative. A stability analysis of the linearized time-fractional Burgers' difference equation was also presented. All linearization strategies used to solve the proposed nonlinear problem are unconditionally stable. To support the theory, two numerical examples are considered. Furthermore, numerical results demonstrate the comparison of linearization strategies and manifest the effectiveness of the proposed numerical scheme in three distinct ways.
  • 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.