Matematik Bölümü Yayın Koleksiyonu

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

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Author: search.filters.author.Singh, Jagdev

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Now showing 1 - 10 of 41
  • 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
  • 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
    Citation - WoS: 2
    Citation - Scopus: 5
    Heat and Mass Transport of Hydromagnetic Williamson Nanofluid Passing Through a Permeable Media Across an Extended Sheet of Varying Thickness
    (Vinca inst Nuclear Sci, 2023) Mehta, Ruchika; Singh, Jagdev; Baleanu, Dumitru; Alshomrani, Ali Saleh; Jangid, Sanju
    The primary goal of this work is to determine heat and mass transfer through fluid-flows sheets dealing mathematical modelling for stagnant and varying thick-ness, considering magnetic fields, permeability, heat source/sink, radiation, Joule heating, chemical reactions, and buoyancy force. The Runge-Kutta fourth order Method (RK-4th order) is used to transform PDE into ODE utilizing similarity con-versions. To tabularize mathematical remarks of the local parameters, RK-4th has been developed in MATLAB. For diverse parameters under diverse constant and changing thickness circumstances of fluid characteristics, Nusselt and Sherwood parameters are examined and quantified. Temperature, velocity, and volume frac-tion graphical representations are used to describe the effects of various factors. When it comes to irregular fluid properties, the coefficient of skin friction has a bigger impact than when it comes to continuous fluid characteristics. However, in the situation of inconstant fluid properties, the local Nusselt number is smaller than in the case of constant fluid characteristics. The RK 4th technique produced high precision computational results, according to the findings.
  • Article
    Citation - WoS: 8
    Citation - Scopus: 15
    Fractional Dynamics and Analysis of Coupled Schrodinger-Kdv Equation With Caputo-Katugampola Type Memory
    (Asme, 2023) Gupta, Arpita; Baleanu, Dumitru; Singh, Jagdev
    Fundamental purpose of the current research article is to analyze the behavior of obtained results of time fractional nonlinear coupled Schrodinger-KdV equation, via implementing an effective analytical technique. In this work, Katugampola fractional derivative in Caputo type is used to model the problem. The coupled Schrodinger-KdV equation describes several kinds of wave propagation in plasma physics, like electromagnetic waves, dust-acoustic waves, and Langmuir waves. The fixed point theorem is used to present the existence and uniuness analysis of obtained solution of the discussed model. Numerical simulation and graphical behavior of the model are presented to show the reliability of the implemented analytical technique. A comparative analysis of exact and obtained approximate solutions is also presented.
  • Article
    Citation - WoS: 8
    Citation - Scopus: 14
    Analysis of the Impact of Thermal Radiation and Velocity Slip on the Melting of Magnetic Hydrodynamic Micropolar Fluid-Flow Over an Exponentially Stretching Sheet
    (Vinca inst Nuclear Sci, 2023) Singh, Jagdev; Mehta, Ruchika; Kumar, Devendra; Baleanu, Dumitru; Kumar, Ravindra
    The belongings of radiation and velocity slip on MHD stream and melting warmth transmission of a micropolar liquid over an exponentially stretched sheet which is fixed in a porous medium with heat source/sink are accessible. Homothety trans-forms the major PDE into a set of non-linear ODE. Then, by varying the boundary value problem to the initial value problem first, we get a numerical solution the non-linear system of equations. It has been observed that related parameters have a significant effect on flow and heat transfer characteristics, which are demonstrat-ed and explained in aspect done their figures. Velocity and temperature decrease by an extension in the magnetic aspect, and the angular velocity increase but the reverse effects come in melting, microrotation, and mixed convection parameters. The surface resistance coefficient as well as couple stress both decreases with amplification in the Eckert number microrotation, material, radiation, and heat source/sink parameter but the heat transport coefficient increase.
  • Article
    Citation - WoS: 32
    Citation - Scopus: 38
    On the Analysis of an Analytical Approach for Fractional Caudrey-Dodd Equations
    (Elsevier, 2022) Gupta, Arpita; Baleanu, Dumitru; Singh, Jagdev
    The principal aim of this paper is to study the approximate solution of nonlinear Caudrey-Dodd-Gibbon equation of fractional order by employing an analytical method. The Caudrey-Dodd-Gibbon equation arises in plasma physics and laser optics. The Caputo derivative is applied to model the physical problem. By applying an effective semi-analytical technique, we attain the approximate solutions without linearization. The uniqueness and the convergence analysis for the applied method are shown. The graphical representation of solutions of fractional Caudrey-Dodd-Gibbon equation demonstrates the applied technique is very efficient to obtain the solutions of such type of fractional order mathematical models. (c) 2021 THE AUTHORS. Published by Elsevier BV on behalf of Faculty of Engineering, Alexandria University. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/ licenses/by-nc-nd/4.0/).
  • Article
    Citation - WoS: 15
    Citation - Scopus: 19
    New Aspects of Fractional Bloch Model Associated With Composite Fractional Derivative
    (Edp Sciences S A, 2021) Kumar, Devendra; Baleanu, Dumitru; Singh, Jagdev
    This paper studies a fractional Bloch equation pertaining to Hilfer fractional operator. Bloch equation is broadly applied in physics, chemistry, nuclear magnetic resonance (NMR), magnetic resonance imaging (MRI) and many more. The sumudu transform technique is applied to obtain the analytic solutions for nuclear magnetization M = (M-x, M-y, M-z). The general solution of nuclear magnetization M is shown in the terms of Mittag-Leffler (ML) type function. The influence of order and type of Hilfer fractional operator on nuclear magnetization M is demonstrated in graphical form. The study of Bloch equation with composite fractional derivative reveals the new features of Bloch equation. The discussed fractional Bloch model provides crucial and applicable results to introduce novel information in scientific and technological fields.
  • Article
    Citation - WoS: 27
    Citation - Scopus: 32
    Fractional Order Continuity of a Time Semi-Linear Fractional Diffusion-Wave System
    (Elsevier, 2020) Luu Vu Cam Hoan; Karapinar, Erdal; Singh, Jagdev; Ho Duy Binh; Nguyen Huu Can; Nguyen Duc Phuong; Hoan, Luu Vu Cam; Binh, Ho Duy; Phuong, Nguyen Duc; Can, Nguyen Huu
    In this work, we consider the time-fractional diffusion equations depend on fractional orders. In more detail, we study on the initial value problems for the time semi-linear fractional diffusion-wave system and discussion about continuity with respect to the fractional derivative order. We find the answer to the question: When the fractional orders get closer, are the corresponding solutions close? To answer this question, we present some depth theories on PDEs and fractional calculus. In addition, we add an example numerical to verify the proposed theory. (C) 2020 The Authors. Published by Elsevier B.V. on behalf of Faculty of Engineering, Alexandria University.