Browsing by Author "Kumar, Sunil"

Now showing 1 - 13 of 13

A fractional derivative with two singular kernels and application to a heat conduction problem
(2020) Baleanu, Dumitru; Jleli, Mohamed; Kumar, Sunil; Samet, Bessem; 56389
In this article, we suggest a new notion of fractional derivative involving two singular kernels. Some properties related to this new operator are established and some examples are provided. We also present some applications to fractional differential equations and propose a numerical algorithm based on a Picard iteration for approximating the solutions. Finally, an application to a heat conduction problem is given.
A fractional order co-infection model between malaria and filariasis epidemic
(2024) Baleanu, Dumitru; Kumar, Ajay; Kumar, Sunil; Baleanu, Dumitru; 56389
In this article, we investigate a mathematical malaria-filariasis co-infection model with the assistance of the non-integer order operator. Using the fractal-fractional operator in the Caputo-Fabrizio (CF) sense, it has been possible to understand the dynamical behaviour and complicatedness of the malaria-filariasis model. An investigation of the existence and uniqueness of the solution employs fixed-point theory. Ulam-Hyers stability helps examine the stability analysis of the proposed co-infection model. The malaria-filariasis model has been investigated using the Toufik-Atanagana (TA), a sophisticated numerical method for these biological co-infection models. With the help of numerical procedures, we provide the approximate solutions for the proposed model. A variety of fractal dimension and fractional order options are utilized for the presentation of the results. When we adjust sensitive parameters like τ and γ, the graphical representation illustrates the system’s behaviour and identifies suitable parameter ranges for solutions. In addition, we evaluate the model along with the regarded operators and various β1 values using an exceptional graphical representation. © 2024 The Author(s). Published by Informa UK Limited, trading as Taylor & Francis Group on behalf of the University of Bahrain.
A modified analytical approach with existence and uniqueness for fractional Cauchy reaction-diffusion equations
(2020) Baleanu, Dumitru; Kumar, Amit; Abbas, Syed; Al Qurashi, Maysaa; Baleanu, Dumitru; 56389
This article mainly explores and applies a modified form of the analytical method, namely the homotopy analysis transform method (HATM) for solving time-fractional Cauchy reaction-diffusion equations (TFCRDEs). Then mainly we address the error norms L2 and L infinity for a convergence study of the proposed method. We also find existence, uniqueness and convergence in the analysis for TFCRDEs. The projected method is illustrated by solving some numerical examples. The obtained numerical solutions by the HATM method show that it is simple to employ. An excellent conformity obtained between the solution got by the HATM method and the various well-known results available in the current literature. Also the existence and uniqueness of the solution have been demonstrated.
A robust study on the listeriosis disease by adopting fractal-fractional operators
(2020) Baleanu, Dumitru; Yavuz, Mehmet; Baleanu, Dumitru; Kumar, Sunil; 56389
Listeriosis is one of the zoonotic diseases affecting most parts of the Sub-Saharan countries. The infection is often transmitted by eating and it can also pass by respiratory and direct contact. In this paper, a listeriosis mathematical model is formulated involving fractal-fractional orders in both Caputo and Atangana-Baleanu derivatives. Moreover, future behaviors of the disease are investigated by considering the fractal-fractional operators that are very effective in modeling the real-life phenomena by virtue of their memory effect. The basic properties and steady states are also obtained. The threshold parameter for determining the spread of the disease is computed. Numerical results are presented for each fractal-fractional-order operator. The results obtained in the paper show that the numerical schemes are effective for predicting and analyzing complex phenomena. (C) 2019 THE AUTHORS. Published by Elsevier BV on behalf of Faculty of Engineering, Alexandria University.
A spectral collocation method for fractional chemical clock reactions
(2020) Baleanu, Dumitru; Saad, Khaled M.; Baleanu, Dumitru; Kumar, Sunil; 56389
We implement an efficient computational scheme to study the effect of precursor consumption on chemical clock reactions. The proposed model is formulated as a system of FDEs with power kernel. This paper considers the fractional derivatives of Liouville-Caputo (LC). We use the spectral collocation method (SCM) with the help of the third-kind Chebyshev polynomials. This scheme generates the fast convergent series solutions with conveniently determinable coefficients. We compute the residual error function (REF) to satisfy the accuracy of the introduced technique. This approach is an easy and efficient tool for implementing the study of such these models. We introduce a comparison between the obtained approximate solutions and those which occurred using a previously published method and excellent agreement is reported.
An Efficient Numerical Method for Fractional SIR Epidemic Model of Infectious Disease by Using Bernstein Wavelets
(2020) Baleanu, Dumitru; Ahmadian, Ali; Kumar, Ranbir; Kumar, Devendra; Singh, Jagdev; Baleanu, Dumitru; Salimi, Mehdi; 56389
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.
Bright, Dark, And Singular Optical Soliton Solutions For Perturbed Gerdjikov-İvanov Equation
(2021) Baleanu, Dumitru; Mustafa, I.N.C.; Baleanu, Dumitru; Kumar, Sunil; 56389
This study consider Gerdjikov-Ivanov equation where the perturbation terms appear with full non-linearity. The Jacobi elliptic function ansatz method is implemented to obtain exact solutions of this equation that models pulse dynamics in optical fibers. It is retrieved some bright, dark optical and singular solitons profile in the limiting cases of the Jacobi elliptic functions. The constraint conditions depending on the parameters for the existence of solitons are also presented. © 2021. Society of Thermal Engineers of Serbia. Published by the Vinča Institute of Nuclear Sciences, Belgrade, Serbia. This is an open access article distributed under the CC BY-NC-ND 4.0 terms and conditions.
Introduction to the Special Issue on Mathematical Aspects of Computational Biology and Bioinformatics
(2023) Baleanu, Dumitru; Pinto, Carla M. A.; Kumar, Sunil; 56389
Nonlinear Dynamics of Cattaneo-Christov Heat Flux Model for Third-Grade Power-Law Fluid
(2020) Baleanu, Dumitru; Kumar, Sunil; Cattani, Carlo; Baleanu, Dumitru; 56389
A rigorous analysis of coupled nonlinear equations for third-grade viscoelastic power-law non-Newtonian fluid is presented. Initially, the governing partial differential equations for conservation of energy and momentum are transformed to nonlinear coupled ordinary differential equations using exact similarity transformations which are known as Cattaneo-Christov heat flux model for third-grade power-law fluid. The homotopy analysis method (HAM) is utilized to approximate the systematic solutions more precisely with shear-thickening, moderately shear-thinning, and most shear-thinning fluids. The solution depends on various parameters including Prandtl number, power index, and temperature variation coefficient. A systematic analysis of boundary-layer flow demonstrates the impact of these parameters on the velocity and temperature profiles.
Projectile motion using three parameter Mittag-Leffler function calculus
(2022) Baleanu, Dumitru; Belgacem, Rachid; Kumar, Sunil; Baleanu, Dumitru; Djilali, Salih; 56389
In the present work, we study the motion of the projectile using the regularized Prabhakar derivative of order β. The correlation of physical quantities with units of measurement creates an obstacle in solving some fractional differential equations, as the solutions presented mathematically may not have a physical meaning. To overcome this problem and maintain dimensions of physical quantities, an auxiliary parameter σ is usually used. We obtain analytical solutions of the velocity fractional differential system in terms of the three parameters Mittag-Leffler function denoted Eα,βγ(z). We recover the cases when applying Caputo and ordinary derivatives.
Residual power series method for time-fractional Schrodinger equations
(Int Scientific Research Publications, 2016) Baleanu, Dumitru; Kumar, Amit; Kumar, Sunil; Baleanu, Dumitru; 56389
In this paper, the residual power series method (RPSM) is effectively applied to find the exact solutions of fractional-order time dependent Schrodinger equations. The competency of the method is examined by applying it to the several numerical examples. Mainly, we find that our solutions obtained by the proposed method are completely compatible with the solutions available in the literature. The obtained results interpret that the proposed method is very effective and simple for handling different types of fractional differential equations (FDEs). (C) 2016 All rights reserved.
Two analytical methods for time-fractional nonlinear coupled Boussinesq-Burger's equations arise in propagation of shallow water waves
(Springer, 2016) Baleanu, Dumitru; Kumar, Amit; Baleanu, Dumitru
In this paper, an analytical method based on the generalized Taylors series formula together with residual error function, namely residual power series method (RPSM), is proposed for finding the numerical solution of the coupled system of time-fractional nonlinear Boussinesq-Burger's equations. The Boussinesq-Burger's equations arise in studying the fluid flow in a dynamic system and describe the propagation of the shallow water waves. Subsequently, the approximate solutions of time-fractional nonlinear coupled Boussinesq-Burger's equations obtained by RPSM are compared with the exact solutions as well as the solutions obtained by modified homotopy analysis transform method. Then, we provide a rigorous convergence analysis and error estimate of RPSM. Numerical simulations of the results are depicted through different graphical representations and tables showing that present scheme is reliable and powerful in finding the numerical solutions of coupled system of fractional nonlinear differential equations like Boussinesq-Burger's equations
Variational iteration method for generalized pantograph equation with convergence analysis
(2014) Baleanu, Dumitru; Baleanu, Dumitru; Karimi, Kobra; Kumar, Sunil; 56389
In this paper, we solve generalized pantograph equation by changing the problem to a system of ordinary equations and using the variational iteration method. We discuss convergence of the proposed method to the exact solution. Finally, illustrative examples are given to demonstrate the efficiency of the method.