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Scopus İndeksli Yayınlar Koleksiyonu

Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651

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Author: search.filters.author.Inc, Mustafa

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Now showing 1 - 10 of 127
  • Article
    Citation - WoS: 14
    Citation - Scopus: 18
    Existence Theory and Numerical Simulation of HIV-I Cure Model with New Fractional Derivative Possessing a Non-Singular Kernel
    (Springeropen, 2019) Aliyu, Aliyu Lsa; Alshomrani, Ali Saleh; Li, Yongjin; Inc, Mustafa; Baleanu, Dumitru
    In this research work, a mathematical model related to HIV-I cure infection therapy consisting of three populations is investigated from the fractional calculus viewpoint. Fractional version of the model under consideration has been proposed. The proposed model is examined by using the Atangana-Baleanu fractional operator in the Caputo sense (ABC). The theory of Picard-Lindelof has been employed to prove existence and uniqueness of the special solutions of the proposed fractional-order model. Further, it is also shown that the non-negative hyper-plane a positively invariant region for the underlying model. Finally, to analyze the results, some numerical simulations are carried out via a numerical technique recently devised for finding approximate solutions of fractional-order dynamical systems. Upon comparison of the numerical simulations, it has been demonstrated that the proposed fractional-order model is more accurate than its classical version. All the necessary computations have been performed using MATLAB R2018a with double precision arithmetic.
  • Article
    On Optical Solitons of the Non-Local Nlse With Time Dependent Coefficients
    (Natl inst Optoelectronics, 2016) Baleanu, Dumitru; Baleanu, Dumitru; Kilic, Bulent; Inc, Mustafa; Matematik
    This paper integrates non-local nonlinear Schrodinger equation (NNLSE) with time dependent coefficients. The first integral method (FIM) is applied to report the optical soliton solutions of NNLSE with parabolic law nonlinearity and time dependent coefficients which are the terms of velocity dipersion, linear and nonlinear terms and also non-local one.
  • Article
    Citation - WoS: 27
    Citation - Scopus: 18
    The First Integral Method for Wu-Zhang Nonlinear System With Time-Dependent Coefficients
    (Editura Acad Romane, 2015) Baleanu, Dumitru; Baleanu, Dumitru; Kilic, Bulent; Inc, Mustafa; Matematik
    The first integral method is used to construct traveling wave solutions of Wu-Zhang nonlinear dynamical system with time-dependent coefficients. We obtained different types of exact solutions by using two types of variable transformations. The method is an effective tool to construct the different types.of exact solutions of nonlinear partial differential equations having real world applications.
  • Article
    Citation - WoS: 35
    Citation - Scopus: 34
    New Optical Solitons of Conformable Resonant Nonlinear Schrodinger's Equation
    (de Gruyter Poland Sp Z O O, 2020) Rezazadeh, Hadi; Abazari, Reza; Khater, Mostafa M. A.; Inc, Mustafa; Baleanu, Dumitru
    Sardar subequation approach, which is one of the strong methods for solving nonlinear evolution equations, is applied to conformable resonant Schrodinger's equation. In this technique, if we choose the special values of parameters, then we can acquire the travelling wave solutions. We conclude that these solutions are the solutions obtained by the first integral method, the trial equation method, and the functional variable method. Several new traveling wave solutions are obtained including generalized hyperbolic and trigonometric functions. The new derivation is of conformable derivation introduced by Atangana recently. Solutions are illustrated with some figures.
  • Article
    Citation - WoS: 23
    Citation - Scopus: 30
    Fractional-Order Dynamics of Human Papillomavirus
    (Elsevier, 2022) Zafar, Zain Ul Abadin; Hussain, M. T.; Inc, Mustafa; Baleanu, Dumitru; Almohsen, Bandar; Oke, Abayomi S.; Javed, Shumaila; Javeed, Shumaila
    Human papillomavirus (HPV) is a reproductive tract infection common to sexually active human. Many of the low-risk HPV infections clear up without any medications but the High-risk HPV-related diseases can remain in the body for a long time. Most of the cases of cervical cancers and other genital cancers are consequences of HPVrelated diseases. As HPV-related diseases are on the increase and controlling the spread is becoming difficult, this present study explores the influence of vaccination on the spread of the diseases. A fractional order mathematical model that captures different HPV risk level is developed in this study. The basic reproduction ratio is obtained for the fractional order model and a locally asymptomatically stable disease-free equilibrium is shown to exist. A comprehensive analysis of the effect of vaccination efficacy and rate of vaccination is carried out and the results indicate that the spread of HPV infection can be mitigated by vaccination.
  • Article
    Citation - WoS: 10
    Citation - Scopus: 12
    Soliton Solutions for Non-Linear Kudryashov's Equation Via Three Integrating Schemes
    (Vinca inst Nuclear Sci, 2021) Mirhosseini-Alizamini, Mehdi; Baleanu, Dumitru; Rezazadeh, Hadi; Inc, Mustafa; Hussain, Majid; Arshed, Saima; Mirhosseini-Alizamini, Seyed Mehdi; Mustafa, I.N.C.
    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 tanh-coth expansion method have been employed for obtaining the desired soliton solutions.
  • Article
    Citation - WoS: 23
    Citation - Scopus: 23
    The Generalized Sasa-Satsuma Equation and Its Optical Solitons
    (Springer, 2022) Hosseini, K.; Sadri, K.; Salahshour, S.; Baleanu, D.; Mirzazadeh, M.; Inc, Mustafa
    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.
  • Article
    Citation - WoS: 69
    Citation - Scopus: 69
    Optical Solitons and Modulation Instability Analysis of an Integrable Model of (2+1)-Dimensional Heisenberg Ferromagnetic Spin Chain Equation
    (Academic Press Ltd- Elsevier Science Ltd, 2017) Aliyu, Aliyu Isa; Yusuf, Abdullahi; Baleanu, Dumitru; Inc, Mustafa
    This paper addresses the nonlinear Schrbdinger 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. (C) 2017 Elsevier Ltd. All rights reserved.
  • Article
    Citation - WoS: 2
    Citation - Scopus: 3
    On Some Novel Optical Solitons To the Cubic-Quintic Nonlinear Helmholtz Model
    (Springer, 2022) Inc, Mustafa; Tariq, Kalim U.; Tchier, Fairouz; Ilyas, Hamza; Baleanu, Dumitru; Khater, Mostafa M. A.
    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 Schrodinger 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.
  • Article
    On Solutions of Variable-Order Fractional Differential Equations
    (Elsevier B.V., 2017) Akgül, Ali; Inc, Mustafa; Baleanu, Dumitru; Abdalla, Bahaaeldin; Jarad, Fahd; Bouchelaghem, Faycal; Abdeljawad, Thabet; Ardjouni, Abdelouaheb; Boulares, Hamid; Shah, Kamal
    Numerical calculation of the fractional integrals and derivatives is the code tosearch fractional calculus and solve fractional differential equations. The exactsolutions to fractional differential equations are compelling to get in real ap-plications, due to the nonlocality and complexity of the fractional differentialoperators, especially for variable-order fractional differential equations. There-fore, it is significant to enhance numerical methods for fractional differentialequations. In this work, we consider variable-order fractional differential equa-tions by reproducing kernel method. There has been much attention in theuse of reproducing kernels for the solutions to many problems in the recentyears. We give an example to demonstrate how efficiently our theory can beimplemented in practice.