Matematik Bölümü Yayın Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/413
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Editorial Citation - WoS: 3Modelling Heat and Mass Transfer Phenomena New Trends in Analytical and Numerical Methods(Vinca inst Nuclear Sci, 2019) Inc, Mustafa; Baleanu, Dumitru; Baleanu, Dumitru; Hristov, Jordan; MatematikEditorial Citation - WoS: 1New Trends in Fractional Modelling of Transport Problems in Fluid Mechanics and Heat Mass Transfer(Vinca inst Nuclear Sci, 2018) Inc, Mustafa; Baleanu, Dumitru; Baleanu, Dumitru; Hristov, Jordan; MatematikArticle On Optical Solitons of the Non-Local Nlse With Time Dependent Coefficients(Natl inst Optoelectronics, 2016) Baleanu, Dumitru; Baleanu, Dumitru; Kilic, Bulent; Inc, Mustafa; MatematikThis 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: 10Citation - Scopus: 12Soliton 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: 14Citation - Scopus: 13Exact Solutions of Stochastic Kdv Equation With Conformable Derivatives in White Noise Environment(Vinca inst Nuclear Sci, 2021) Inc, Mustafa; Baleanu, Dumitru; Ulutas, EsmaIn 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: 10Citation - Scopus: 9Bright, 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: 8Citation - Scopus: 8Dynamical Behaviour of the Joseph-Egri Equation(Vinca inst Nuclear Sci, 2023) Inc, Mustafa; Leta, Temesgen D.; Baleanu, Dumitru; Rezazade, Hadi; Sabi'u, Jamilu; Rezazadeh, Hadi; Sabi’u, JamiluWe investigate traveling wave solutions to the Joseph-Egri equation via extended auxiliary equation technique. We have determined stationary points of the dynamical systems by using bifurcation method. We also acquire cusp, periodic and homoclinic orbits. The investigated solutions are entirely different from the reported in the liter-ature. However, some of the reported solutions are plotted to understand the physical application of the considered model using renowned mathematical software.Article Citation - WoS: 6Citation - Scopus: 7On Fractional Kdv-Burgers and Potential Kdv Equations Existence and Uniqueness Results(Vinca inst Nuclear Sci, 2019) Inc, Mustafa; Baleanu, Dumitru; Hashemi, Mir SajjadRecently a new kind of derivatives, namely the conformable derivative is introduced which have not many drawbacks of other fractional derivatives. Two types of KdV equations with conformable derivative are investigated in this paper. Existence and uniqueness of two different equations of KdV class with conformable derivatives are investigated. It is also shown that the invariant subspace method can be extended to find the exact solutions of these equations.Article Citation - WoS: 13Citation - Scopus: 15N-Wave and Other Solutions To the B-Type Kadomtsev-Petviashvili Equation(Vinca inst Nuclear Sci, 2019) Hosseini, Kamyar; Samavat, Majid; Mirzazadeh, Mohammad; Eslami, Mostafa; Moradi, Mojtaba; Baleanu, Dumitru; Inc, MustafaThe present article studies a B-type Kadomtsev-Petviashvili equation with certain applications in the fluids. Stating with the Hirota's bilinear form and adopting reliable methodologies, a group of exact solutions such as the N-wave and other solutions to the B-type Kadomtsev-Petviashvili equation is formally derived. Some figures in two and three dimensions are given to illustrate the characteristics of the obtained solutions. The results of the current work actually help to complete the previous studies about the B-type Kadomtsev-Petviashvili equation.Article Citation - WoS: 17Citation - Scopus: 17Yficitious Time Integration Method for Solving the Time Fractional Gas Dynamics Equation(Vinca inst Nuclear Sci, 2019) Inc, Mustafa; Baleanu, Dumitru; Moshokoa, Seithuti Philemon; Partohaghighi, MohammadIn this work a poweful approach is presented to solve the time-fractional gas dynamics equation. In fact, we use a fictitious time variable y to convert the dependent variable w(x, t) into a new one with one more dimension. Then by taking a initial guess and implementing the group preserving scheme we solve the problem. Finally four examples are solved to illustrate the power of the offered method.