Browsing by Author "Singh, Jagdev"

Now showing 1 - 20 of 41

Citation - WoS: 43
Citation - Scopus: 52
Analysis and Dynamics of Fractional Order Covid-19 Model With Memory Effect
(Elsevier, 2021) Kumar, Devendra; Singh, Jagdev; Baleanu, Dumitru; Yadav, Supriya; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
The present article attempts to examine fractional order Covid-19 model by employing an efficient and powerful analytical scheme termed as q-homotopy analysis Sumudu transform method (q-HASTM). The q-HASTM is the hybrid scheme based on q-HAM and Sumudu transform technique. Liouville-Caputo approach of the fractional operator has been employed. The proposed modelis also examined numerically via generalized Adams-Bashforth-Moulton method. We determined model equilibria and also give their stability analysis by employing next generation matrix and fractional Routh-Hurwitz stability criterion.
Citation - WoS: 99
Citation - Scopus: 116
Analysis of a Fractional Model of the Ambartsumian Equation
(Springer Heidelberg, 2018) Singh, Jagdev; Baleanu, Dumitru; Rathore, Sushila; Kumar, Devendra; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
The prime target of this work is to investigate a fractional model of the Ambartsumian equation. This equation is very useful to describe the surface brightness of the Milky Way. The Ambartsumian equation of fractional order is solved with the aid of the HATM. The solution is presented in terms of the power series, which is convergent for all real values of variables and parameters. The outcomes drawn with the help of the HATM are presented in the form of graphs.
Citation - WoS: 30
Citation - Scopus: 33
Analysis of a New Fractional Model for Damped Bergers' Equation
(de Gruyter Open Ltd, 2017) Kumar, Devendra; Al Qurashi, Maysaa; Baleanu, Dumitru; Singh, Jagdev; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
In this article, we present a fractional model of the damped Bergers' equation associated with the Caputo-Fabrizio fractional derivative. The numerical solution is derived by using the concept of an iterative method. The stability of the applied method is proved by employing the postulate of fixed point. To demonstrate the effectiveness of the used fractional derivative and the iterative method, numerical results are given for distinct values of the order of the fractional derivative.
Citation - WoS: 66
Citation - Scopus: 86
Analysis of Fractional Model of Guava for Biological Pest Control With Memory Effect
(Elsevier, 2021) Ganbari, Behzad; Kumar, Devendra; Baleanu, Dumitru; Singh, Jagdev; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
Introduction: Fractional operators find their applications in several scientific and engineering processes. We consider a fractional guava fruit model involving a non-local additionally non-singular fractional derivative for the interaction into guava pests and natural enemies. The fractional guava fruit model is considered as a Lotka-Volterra nature. Objectives: The main objective of this work is to study a guava fruit model associated with a non-local additionally non-singular fractional derivative for the interaction into guava pests and natural enemies. Methods: Existence and uniqueness analysis of the solution is evaluated effectively by using Picard Lindelof approach. An approximate numerical solution of the fractional guava fruit problem is obtained via a numerical scheme. Results: The positivity analysis and equilibrium analysis for the fractional guava fruit model is discussed. The numerical results are demonstrated to prove our theoretical results. The graphical behavior of solution of the fractional guava problem at the distinct fractional order values and at various parameters is discussed. Conclusion: The graphical behavior of solution of the fractional guava problem at the distinct fractional order values and at various parameters shows new vista and interesting phenomena of the model. The results are indicating that the fractional approach with non-singular kernel plays an important role in the study of different scientific problems. The suggested numerical scheme is very efficient for solving nonlinear fractional models of physical importance. (C) 2021 The Authors. Published by Elsevier B.V. on behalf of Cairo University.
Citation - WoS: 46
Citation - Scopus: 49
Analysis of Logistic Equation Pertaining To a New Fractional Derivative With Non-Singular Kernel
(Sage Publications Ltd, 2017) Singh, Jagdev; Al Qurashi, Maysaa; Baleanu, Dumitru; Kumar, Devendra; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
In this work, we aim to analyze the logistic equation with a new derivative of fractional order termed in Caputo-Fabrizio sense. The logistic equation describes the population growth of species. The existence of the solution is shown with the help of the fixed-point theory. A deep analysis of the existence and uniqueness of the solution is discussed. The numerical simulation is conducted with the help of the iterative technique. Some numerical simulations are also given graphically to observe the effects of the fractional order derivative on the growth of population.
Citation - WoS: 197
Citation - Scopus: 208
Analysis of Regularized Long-Wave Equation Associated With a New Fractional Operator With Mittag-Leffler Type Kernel
(Elsevier, 2018) Singh, Jagdev; Baleanu, Dumitru; Sushila; Kumar, Devendra; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
In this work, we aim to present a new fractional extension of regularized long-wave equation. The regularized long-wave equation is a very important mathematical model in physical sciences, which unfolds the nature of shallow water waves and ion acoustic plasma waves. The existence and uniqueness of the solution of the regularized long-wave equation associated with Atangana Baleanu fractional derivative having Mittag-Leffler type kernel is verified by implementing the fixed-point theorem. The numerical results are derived with the help of an iterative algorithm. In order to show the effects of various parameters and variables on the displacement, the numerical results are presented in graphical and tabular form. (C) 2017 Elsevier B.V. All rights reserved.
Citation - WoS: 7
Citation - Scopus: 13
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; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
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.
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; 56389; Matematik; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
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.
Citation - WoS: 19
Citation - Scopus: 51
Computational Study of Fractional Order Smoking Model
(Pergamon-elsevier Science Ltd, 2021) Baleanu, Dumitru; Singh, Jagdev; Dutta, Hemen; Singh, Harendra; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
Smoking is a very challenging problem the world is facing every day. It contributes to deaths and major health problems to millions of people every year around the world. A lot of work has been devoted to study how to minimize smoking in the society. Here we study non-integer order smoking model using an iterative scheme which is combination of discretization of domain and short memory principle. We will also discuss stability of the proposed model and used iterative scheme. CPU time is listed in tabular to show the efficiency and figures are used to show behaviour of solution in long time. The proposed technique has high accuracy and low computational cost. Using figures fractional time behaviour of solution is also plotted. (C) 2020 Published by Elsevier Ltd.
Editorial for the Mmas Special Issue "role of Fractional Operators and Mathematical Modelling in Applied Sciences
(Wiley, 2023) Kumar, Devendra; Baleanu, Dumitru; Singh, Jagdev; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
Citation - WoS: 57
Citation - Scopus: 72
An Efficient Computational Approach for Local Fractional Poisson Equation in Fractal Media
(Wiley, 2021) Ahmadian, Ali; Rathore, Sushila; Kumar, Devendra; Baleanu, Dumitru; Salimi, Mehdi; Salahshour, Soheil; Singh, Jagdev; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
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 - WoS: 70
Citation - Scopus: 81
An Efficient Computational Technique for Fractal Vehicular Traffic Flow
(Mdpi, 2018) Tchier, Fairouz; Singh, Jagdev; Baleanu, Dumitru; Kumar, Devendra; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
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 - WoS: 53
Citation - Scopus: 58
An Efficient Computational Technique for Fractional Model of Generalized Hirota-Satsuma Korteweg-De Vries and Coupled Modified Korteweg-De Vries Equations
(Asme, 2020) Prakasha, D. G.; Kumar, Devendra; Baleanu, Dumitru; Singh, Jagdev; Veeresha, P.; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
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 algorithm. The achieved results illuminate that, the suggested computational method is very effective to investigate the considered fractional-order model.
Citation - WoS: 140
Citation - Scopus: 156
An Efficient Numerical Algorithm for the Fractional Drinfeld-Sokolov Equation
(Elsevier Science inc, 2018) Kumar, Devendra; Baleanu, Dumitru; Rathore, Sushila; Singh, Jagdev; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
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 - WoS: 180
Citation - Scopus: 198
An Efficient Numerical Method for Fractional Sir Epidemic Model of Infectious Disease by Using Bernstein Wavelets
(Mdpi, 2020) Ahmadian, Ali; Kumar, Ranbir; Kumar, Devendra; Singh, Jagdev; Baleanu, Dumitru; Salimi, Mehdi; Kumar, Sunil; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
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.
Citation - WoS: 7
Citation - Scopus: 14
Fractional Dynamics and Analysis of Coupled Schrodinger-Kdv Equation With Caputo-Katugampola Type Memory
(Asme, 2023) Gupta, Arpita; Baleanu, Dumitru; Singh, Jagdev; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
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.
Citation - WoS: 36
Citation - Scopus: 44
Fractional Klein-Gordon Equations With Mittag-Leffler Memory
(Elsevier, 2020) Prakasha, D. G.; Singh, Jagdev; Kumar, Devendra; Baleanu, Dumitru; Veeresha, P.; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
The main objective of the present investigation is to find the solution for the fractional model of Klein-Gordon-Schrodinger system with the aid of q-homotopy analysis transform method (q-HATM). The projected solution procedure is an amalgamation of q-HAM with Laplace transform. More preciously, to elucidate the effectiveness of the projected scheme we illustrate the response of the q-HATM results, and the numerical simulation is offered to guarantee the exactness. Further, the physical behaviour has been presented associated with parameters present the method with respect fractional-order. The present study confirms that, the projected solution procedure is highly methodical and accurate to solve and study the behaviours of the system of differential equations with arbitrary order exemplifying the real word problems.
Citation - WoS: 62
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; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
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 - WoS: 27
Citation - Scopus: 29
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; 19184; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
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.
Citation - WoS: 9
Citation - Scopus: 18
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; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
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.