Numerical simulations for fractional variation of (1?+?1)-dimensional Biswas-Milovic equation

In this work, the residual power series method (RPSM) is used to solve fractional variation of (1 + 1)-dimensional Biswas-Milovic equation that defines the long-space optical communications. The RPSM gets Maclaurin expansion of the solution. The solutions of present equation are computed in the shape of quickly convergent series with quickly calculable fundamentals by using mathematica software package. Explanation of the method is given graphical consequens and series solutions are made use of to represent our solution. The found consequens show that technique is a power ansd efficient method in conviction of solution for the fractional (1 + 1)-dimensional Biswas-Milovic equation. © 2018 Elsevier Gmb

Maxwellian evolution equations along the uniform optical fiber in Minkowski space

WOS:000574870900006We firstly discuss the geometric phase rotation for an electromagnetic wave traveling along with the optical fiber in Minkowski space. We define two novel types of geometric phases associated with the evolution of the polarization vectors in the normal and binormal directions along with the optical fiber. We also identify the normal-Rytov parallel transportation law and binormal-Rytov parallel transportation law. Moreover, we derive their relationships with the Fermi-Walker transportation law in Minkowski space. Then we solve Maxwell's equations by using geometric quantities associated with the curved path, which characterizes the optical fiber. Finally, we investigate that electromagnetic wave propagation admits the Maxwellian evolution equation for the anholonomic coordinate system in Minkowski space

A New İterative Algorithm on the Time-Fractional Fisher Equation: Residual Power Series Method

In this article, the residual power series method is used to solve time-fractional Fisher equation. The residual power series method gets Maclaurin expansion of the solution. The solutions of present equation are computed in the shape of quickly convergent series with quickly calculable fundamentals using mathematica software package. Explanation of the method is given by graphical consequences and series solutions are made use of to represent our solution. The found consequences show that technique is a power and efficient method in conviction of solution time-fractional Fisher equation. © The Author(s) 2017.The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work was funded by the International Scientific Partnership Program ISPP at King Saud University (ISPP# 63)

New Soliton Solutions of the Fractional Regularized Long Wave Burger Equation By Means of Conformable Derivative

In this paper, the practice of the extended direct algebraic method (EDAM) is used to solve fractional Regularized Long Wave Burgers (RLW-Burgers) equation by means of the conformable derivative. Firstly, this fractional equation is changed into the ordinary differential equation by using the traveling wave transformation. Then new soliton solutions are obtained by using EDAM. This presented form is important in physics and engineering. The created soliton solutions play a major task for scientists about an agreement the physical event of this equation. The graphics of some solutions are drawn at fitting values of parameters. The obtained outcomes appear clarity, accuracy, and potentiality of the presented scheme. © 2019King Saud University Deanship of Scientific Research, King Saud University Female Center for Scientific and Medical Colleges, King Saud UniversityThis research project was supported by a grant from the Research Center of the Center for Female Scientific and Medical Colleges, Deanship of Scientific Research , King Saud University . Appendix

New Solutions of the Fractional Boussinesq-Like Equations By Means of Conformable Derivatives

In this paper, the process of the extended direct algebraic method (EDAM) is used to solve two fractional Boussinesq-like equations by means of conformable derivatives. Firstly, these fractional equations are changed into the ordinary differential equations by using the traveling wave transformation. Then new solutions are obtained by using EDAM. This dynamical model plays a key role in engineering and physics. The constructed solitons solution help researchers in understanding the physical phenomenon of this equation. The standard linear stability analysis is utilized and the stability of the model is investigated which substantiate that all results are stable and exact. Graphically, the movements of some solutions are depicted at appropriate values of parameters. The achieved results show simplicity, reliability, and power of the current schemes. © 2019 The AuthorsKing Saud University Deanship of Scientific Research, King Saud University Female Center for Scientific and Medical Colleges, King Saud UniversityThis research project was supported by a grant from the Research Center of the Center for Female Scientific and Medical Colleges, Deanship of Scientific Research, King Saud University. Appendix