Browsing by Author "Inc, Mustafa"

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A delayed plant disease model with Caputo fractional derivatives
(2022) Baleanu, Dumitru; Baleanu, Dumitru; Erturk, Vedat Suat; Inc, Mustafa; Govindaraj, V.; 56389
We analyze a time-delay Caputo-type fractional mathematical model containing the infection rate of Beddington–DeAngelis functional response to study the structure of a vector-borne plant epidemic. We prove the unique global solution existence for the given delay mathematical model by using fixed point results. We use the Adams–Bashforth–Moulton P-C algorithm for solving the given dynamical model. We give a number of graphical interpretations of the proposed solution. A number of novel results are demonstrated from the given practical and theoretical observations. By using 3-D plots we observe the variations in the flatness of our plots when the fractional order varies. The role of time delay on the proposed plant disease dynamics and the effects of infection rate in the population of susceptible and infectious classes are investigated. The main motivation of this research study is examining the dynamics of the vector-borne epidemic in the sense of fractional derivatives under memory effects. This study is an example of how the fractional derivatives are useful in plant epidemiology. The application of Caputo derivative with equal dimensionality includes the memory in the model, which is the main novelty of this study.
Complex traveling-wave and solitons solutions to the Klein-Gordon-Zakharov equations
(2020) Baleanu, Dumitru; Abbagari, Souleymanou; Salathiel, Yakada; Inc, Mustafa; Doka, Serge Y.; Crepin, Kofane Timoleon; Baleanu, Dumitru; 56389
This paper studies complex solutions and solitons solutions to the Klein-Gordon-Zakharov equations (KGZEs). Solitons solutions including bright, dark, W-shape bright, breather also trigonometric function solutions and singular solutions of KGZEs are obtained by three integration algorithm. From the spatio-temporal and 3-D and 2-D contour plot, it is observed that obtained solutions move without any deformation that implies the steady state of solutions. Furthermore, these solutions will be helpful to explain the interactions in hight frequency plasma and solitary wave theory.
Dynamical Behaviour Of The Joseph-Egri Equation
(2023) Baleanu, Dumitru; Inc, Mustafa; Leta, Temesgen D.; Baleanu, Dumitru; Rezazadeh, Hadi; 56389
Extended Auxiliary Equation Technique
Exact Solutıons Of Stochastıc Kdv Equatıon Wıth Conformable Derıvatıves In Whıte Noıse Envıronment
(2021) Baleanu, Dumitru; Inc, Mustafa; Baleanu, Dumitru; 56389
In this article, we have considered Wick-type stochastic Korteweg de Vries (KdV) equation with conformable derivatives. By the help of white noise analysis, Hermit transform and extended G′/G-expansion method, we have obtained exact travelling wave solutions of KdV equation with conformable derivatives. We have applied the inverse Hermit transform for stochastic soliton solutions and then we have shown how stochastic solutions can be presented as Brownian motion functional solutions by an application example.
Impact of activation energy and MHD on Williamson fluid flow in the presence of bioconvection
(2022) Baleanu, Dumitru; Zahid, Muhammad; Inc, Mustafa; Baleanu, Dumitru; Almohsen, Bandar; 56389
The main purpose of the current study is to invetigate the influence of Brownian motion and thermophoresis diffusion in non-Newtonian Williamson fluid flow through exponentially stretching sheet with the effects of thermal radiation and the bioconvection of microorganisms. For this purpose, similarity functions are involved to transmute partial differential equations to corresponding ordinary differential equations. Then Runge–Kutta method with shooting technique is hired to evaluate the desired findings with utilization of MATLAB script. The fluid velocity becomes slow against strength of magnetic parameter and it boosts with mixed convection. The temperature rises with parameter of Brownian motion and thermophoresis. The bioconvection Lewis number diminishes the velocity field. Compared with the existing literature, the results show satisfactory congruence's.
Mellin transform for fractional integrals with general analytic kernel
(2022) Baleanu, Dumitru; Kalsoom, Amna; Sager, Maria; Inc, Mustafa; Baleanu, Dumitru; Alshomrani, Ali S.; 56389
Many different operators of fractional calculus have been proposed, which can be organized in some general classes of operators. According to this study, the class of fractional integrals and derivatives can be classified into two main categories, that is, with and without general analytical kernel (introduced in 2019). In this article, we define the Mellin transform for fractional differential operator with general analytic kernel in both Riemann-Liouville and Caputo derivatives of order ς ≥ 0 and ϱ be a fixed parameter. We will also establish relation between Mellin transform with Laplace and Fourier transforms.
New Solitary Wave Solutions for Variants of (3+1)-Dimensional Wazwaz-Benjamin-Bona-Mahony Equations
(2020) Baleanu, Dumitru; Inc, Mustafa; Baleanu, Dumitru; 56389
We solve distinct forms of (3+1)-Dimensional Wazwaz-Benjamin-Bona-Mahony [(3+1)-Dimensional WBBM] equations by employing the method of Sardar-subequation. When parameters involving this approach are taken to be special values, we can obtain the solitary wave solutions (sws) which is concluded from other approaches such as the functional variable method, the trail equation method, the first integral method and so on. We obtain new and general solitary wave solutions in terms of generalized hyperbolic and trigonometric functions. The results demonstrate the power of the proposed method for the determination of sws of non-linear evolution equations (NLEs).
On Numerical Solution of the Time Fractional Advection-Diffusion Equation Involving Atangana-Baleanu-Caputo Derivative
(2020) Baleanu, Dumitru; Inc, Mustafa; Bayram, Mustafa; Baleanu, Dumitru; 56389
A powerful algorithm is proposed to get the solutions of the time fractional Advection-Diffusion equation(TFADE): ABCDβ 0+, t u(x,t) = ζuxx(x,t) - κux(x,t) + F(x, t), 0 < β ≤ 1. The time-fractional derivative ABCDβ 0 + ,t u(x,t) is described in the Atangana-Baleanu Caputo concept. The basis of our approach is transforming the original equation into a new equation by imposing a transformation involving a fictitious coordinate. Then, a geometric scheme namely the group preserving scheme (GPS) is implemented to solve the new equation by taking an initial guess. Moreover, in order to present the power of the presented approach some examples are solved, successfully. © 2019 M. Partohaghighi et al.
On some novel optical solitons to the cubic–quintic nonlinear Helmholtz model
(2022) Baleanu, Dumitru; Inc, Mustafa; Tariq, Kalim U.; Tchier, Fairouz; Ilyas, Hamza; Baleanu, Dumitru; 56389
The purpose of this study is to employ the Sine–Cosine expansion approach to produce some new sort of soliton solutions for the cubic–quintic nonlinear Helmholtz problem. The nonlinear complex model compensates for backward scattering effects that are overlooked in the more popular nonlinear Schrödinger equation. As a result, a number of novel traveling wave structures have been discovered. We also investigate the stability of solitary wave solutions for the governing model. Furthermore, the modulation instability is discussed by employing the standard linear-stability analysis. The 3D, contour and 2D graphs are visualized for several fascinating exact solutions to comprehend their behaviour.
Optical solitons and modulation instability analysis of an integrable model of (2+1)-Dimensional Heisenberg ferromagnetic spin chain equation
(2017) Baleanu, Dumitru; Aliyu, Aliyu Isa; Yusuf, Abdullahi; Baleanu, Dumitru; 56389
This paper addresses the nonlinear Schrödinger type equation (NLSE) in (2+1)-dimensions which describes the nonlinear spin dynamics of Heisenberg ferromagnetic spin chains (HFSC) with anisotropic and bilinear interactions in the semiclassical limit. Two integration schemes are employed to study the equation. These are the complex envelope function ansatz and the generalized tanh methods. Dark, dark-bright or combined optical and singular soliton solutions of the equation are derived. Furthermore, the modulational instability (MI) is studied based on the standard linear-stability analysis and the MI gain is got. Numerical simulation of the obtained results are analyzed with interesting figures showing the physical meaning of the solutions.
Residual power series algorithm for fractional cancer tumor models
(2020) Baleanu, Dumitru; Inc, Mustafa; Hincal, Evren; Baleanu, Dumitru; 56389
In this paper, the new series solutions of some fractional cancer tumor models are investigated by using residual power series method (RPSM). The RPSM is explained with Maclaurin expansion for the solution. One of the advantages of this method is quick and easy calculation to find series solutions by using mathematica software package. Graphical presentations for series solutions are given to explanation of the method. The obtained outcomes explain that process is applicable and reliable method to obtain numerical solutions of fractional equations. (C) 2020 The Authors. Published by Elsevier B.V. on behalf of Faculty of Engineering, Alexandria University.
Soliton Solutions For Non-Linear Kudryashov's Equation Via Three Integrating Schemes
(2021) Baleanu, Dumitru; Mirhosseini-Alizamini, Mehdi; Baleanu, Dumitru; Rezazadeh, Hadi; Inc, Mustafa; Hussain, Majid; 56389
This paper considers the non-linear Kudryashov's equation, that is an extension of the well-known dual-power law of refractive index and is analog to the generalized version of anti-cubic non-linearity. The model is considered in the presence of full non-linearity. The main objective of this paper is to extract soliton solutions of the proposed model. Three state-of-the-art integration schemes, namely modified auxiliary equation method, the sine-Gordon expansion method and the tanhcoth expansion method have been employed for obtaining the desired soliton solutions.
The generalized Sasa–Satsuma equation and its optical solitons
(2022) Hosseini, K.; Sadri, K.; Salahshour, S.; Baleanu, D.; Mirzazadeh, M.; Inc, Mustafa; 56389
The principal goal of the presented paper is to investigate the dynamics of optical solitons for the generalized Sasa–Satsuma (GSS) equation describing the propagation of the femtosecond pulses in the systems of optical fiber transmission. More precisely, the governing model, which is a generalized version of the classical Sasa–Satsuma equation, is firstly reduced in a one-dimensional real regime through a specific transformation; then, its bright and dark optical solitons are established using the modified Kudryashov (MK) method. The changes in the amplitude of the bright and dark solitons are analyzed as a case study for various classes of free parameters. Considerable changes are observed in the optical solitons amplitude from the results presented in the current study.