Browsing by Author "Machado, J. A. T."

Now showing 1 - 4 of 4

Citation - WoS: 192
Citation - Scopus: 218
Fractional Calculus: a Survey of Useful Formulas
(Springer Heidelberg, 2013) Trujillo, J. J.; Rivero, M.; Machado, J. A. T.; Baleanu, D.; Valerio, D.; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
This paper presents a survey of useful, established formulas in Fractional Calculus, systematically collected for reference purposes.
Citation - WoS: 20
Citation - Scopus: 20
On Distinctive Solitons Type Solutions for Some Important Nonlinear Schrodinger Equations
(Springer, 2021) Machado, J. A. T.; Baleanu, D.; Zafar, A.; Raheel, M.; Osman, M. S.; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
The extended Jacobi elliptic function expansion (EJEFE) method is used to retrieve several types of optical solitons of two nonlinear Schrodinger equations, namely the Heisenberg ferromagnetic spin chains and Alfven envelop equations. The obtained traveling wave solutions and the corresponding plots are analysed by means of the symbolic package Mathematica. The solutions show that the proposed strategy is effective and reliable for solving different types of nonlinear differential equations.
Citation - WoS: 85
Citation - Scopus: 82
On Nonautonomous Complex Wave Solutions Described by the Coupled Schrodinger-Boussinesq Equation With Variable-Coefficients
(Springer, 2018) Machado, J. A. T.; Baleanu, Dumitru; Osman, M. S.; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
This paper investigates the coupled Schrodinger-Boussinesq equation with variable-coefficients using the unified method. New nonautonomous complex wave solutions are obtained and classified into two categories, namely polynomial function and rational function solutions. For the polynomial functions emerge the complex solitary, complex soliton and complex elliptic wave solutions, while for the rational function are observed complex periodic rational and complex hyperbolic rational wave solutions. The physical insight and the dynamical behavior of the solutions describing the wave propagation in laser or plasma physics are discussed and analysed for different choices of the arbitrary functions in the solutions.
Citation - WoS: 147
Traveling Wave Solutions To Nonlinear Directional Couplers by Modified Kudryashov Method
(Iop Publishing Ltd, 2020) Baleanu, D.; Machado, J. A. T.; Osman, M. S.; Rezazadeh, H.; Arshed, S.; Gunerhan, H.; Srivastava, H. M.; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
This work finds several new traveling wave solutions for nonlinear directional couplers with optical metamaterials by means of the modified Kudryashov method. This model can be used to distribute light from a main fiber into one or more branch fibers. Two forms of optical couplers are considered, namely the twin- and multiple- core couplers. These couplers, which have applications as intensity-dependent switches and as limiters, are studied with four nonlinear items namely the Kerr, power, parabolic, and dual-power laws. The restrictions on the parameters for the existence of solutions are also examined. The 3D- and 2D figures are introduced to discuss the physical meaning for some of the gained solutions. The performance of the method shows the adequacy , power, and ability for applying to many other nonlinear evolution models.