Scopus İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651
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Review Variational principles in the frame of certain generalized fractional derivatives(Amer Inst Mathematical Sciences-AIMS, 2020) Jarad, Fahd; Abdeljawad, ThabetIn this article, we study generalized fractional derivatives that contain kernels depending on a function on the space of absolute continuous functions. We generalize the Laplace transform in order to be applicable for the generalized fractional integrals and derivatives and apply this transform to solve some ordinary differential equations in the frame of the fractional derivatives under discussion.Article Optical solitons to the (n+1)-dimensional nonlinear Schrodinger's equation with Kerr law and power law nonlinearities using two integration schemes(World Scientific Publ Co Pte Ltd, 2019) İnç, Mustafa; Aliyu, Aliyu Isa; Yusuf, Abdullahi; Bayram, Mustafa; Baleanu, DumitruIn this study, two integration techniques are employed to reach optical solitons to the (n + 1)-dimensional nonlinear Schrodinger's equation ((n + 1)-NLSE) with Kerr and power laws nonlinearities. These are the undetermined coefficient and Bernoulli sub-ODE methods. We acquired bright, dark, and periodic singular soliton solutions. The necessary conditions for the existence of these solitons are presented.Article Optical solitary waves and conservation laws to the (2+1)-dimensional hyperbolic nonlinear Schrodinger equation(World Scientific Publ Co Pte Ltd, 2018) Aliyu, Aliyu Isa; İnç, Mustafa; Yusuf, Abdullahi; Baleanu, DumitruThis work studies the hyperbolic nonlinear Schrodinger equation (H-NLSE) in (2 + 1)-dimensions. The model describes the evolution of the elevation of water wave surface for slowly modulated wave trains in deep water in hydrodynamics, and also governs the propagation of electromagnetic fields in self-focusing and normally dispersive planar wave guides in optics. A class of gray and black optical solitary wave solutions of the H-NLSE are reported by adopting an appropriate solitary wave ansatz solution. Moreover, classification of conservation laws (Cls) to the H-NLSE is implemented using the multipliers approach. Some physical interpretations and analysis of the results obtained are also presented.Article Citation - Scopus: 4Nonlinear singular p-Laplacian boundary value problems in the frame of conformable derivative(American Institute of Mathematical Sciences, 2021) Bouloudene, Mokhtar; Alqudah, Manar A.; Jarad, Fahd; Adjabi, Yassine; Abdeljawad, ThabetThis paper studies a class of fourth point singular boundary value problem of p-Laplacian operator in the setting of a specific kind of conformable derivatives. By using the upper and lower solutions method and fixed point theorems on cones., necessary and sufficient conditions for the existence of positive solutions are obtained. In addition, we investigate the dependence of the solution on the order of the conformable differential equation and on the initial conditions. © 2021 American Institute of Mathematical Sciences. All rights reserved.Article Improved (G'/G)-expansion method for the time-fractional biological population model and Cahn-Hilliard equation(ASME, 2015) Baleanu, Dumitru; Uǧurlu, Yavuz; İnç, Mustafa; Kılıç, BülentIn this paper, we used improved (G'/G)-expansion method to reach the solutions for some nonlinear time-fractional partial differential equations (fPDE). The fPDE is reduced to an ordinary differential equation (ODE) by means of Riemann-Liouille derivative and a basic variable transformation. Various types of functions are obtained for the time-fractional biological population model (fBPM) and Cahn-Hilliard (fCH) equation. Copyright © 2015 by ASME.