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, MustafaCOAR Access Rights: search.filters.coarAccessRights.open access

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Now showing 1 - 10 of 58
  • 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
    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
    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.
  • Article
    Citation - WoS: 1
    Citation - Scopus: 1
    Mellin Transform for Fractional Integrals With General Analytic Kernel
    (Amer inst Mathematical Sciences-aims, 2022) Kalsoom, Amna; Sager, Maria; Inc, Mustafa; Baleanu, Dumitru; Alshomrani, Ali S.; Rashid, Maliha
    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 sigma >= 0 and. be a fixed parameter. We will also establish relation between Mellin transform with Laplace and Fourier transforms.
  • Article
    Citation - WoS: 14
    Citation - Scopus: 13
    Exact Solutions of Stochastic Kdv Equation With Conformable Derivatives in White Noise Environment
    (Vinca inst Nuclear Sci, 2021) Inc, Mustafa; Baleanu, Dumitru; Ulutas, Esma
    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.
  • Article
    Citation - WoS: 91
    Citation - Scopus: 105
    Impact of Activation Energy and Mhd on Williamson Fluid Flow in the Presence of Bioconvection
    (Elsevier, 2022) Zahid, Muhammad; Inc, Mustafa; Baleanu, Dumitru; Almohsen, Bandar; Asjad, Muhammad Imran
    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. (c) 2022 The Authors. Published by Elsevier B.V. on behalf of Faculty of Engineering, Alexandria University This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/
  • Article
    Citation - WoS: 10
    Citation - Scopus: 9
    Bright, Dark, and Singular Optical Soliton Solutions for Perturbed Gerdjikov-Ivanov Equation
    (Vinca inst Nuclear Sci, 2021) Inc, Mustafa; Baleanu, Dumitru; Kumar, Sunil; Ulutas, Esma; Mustafa, I.N.C.
    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.
  • Article
    Citation - WoS: 47
    Citation - Scopus: 52
    A Delayed Plant Disease Model With Caputo Fractional Derivatives
    (Springer, 2022) Baleanu, Dumitru; Erturk, Vedat Suat; Inc, Mustafa; Govindaraj, V; Kumar, Pushpendra
    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.