Alegre and Marin [C. Alegre, J. Marin, Topol. Appl., 203 (2016), 32-41] introduced the concept of modified ω-distance mappings on a complete quasi metric space in which they studied some fixed point results. In this manuscript, we prove some fixed point results of nonlinear contraction conditions through modified ω-distance mapping on a complete quasi metric space in sense of Alegre and Marin.

Abstract:The aim of this paper is to investigate the solution of timefractional coupled degenerate Hamiltonian equations. We use the G ′ /G expansion method to determine soliton solutions of this system for different values of the fractional order.

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The present article is designed to supply two different numerical<br />solutions for solving  Kuramoto-Sivashinsky equation. We have made<br />an attempt to develop a numerical solution via the use of<br />Sinc-Galerkin method for  Kuramoto-Sivashinsky equation, Sinc<br />approximations to both derivatives and indefinite integrals reduce<br />the solution to an explicit system of algebraic equations. The fixed<br />point theory is used to prove the convergence of the proposed<br />methods. For comparison purposes, a combination of a Crank-Nicolson<br />formula in the time direction, with the Sinc-collocation in the<br />space direction is presented, where the derivatives in the space<br />variable are replaced by the necessary matrices to produce a system<br />of algebraic equations. In addition, we present numerical examples<br />and comparisons to support the validity of these proposed<br />methods.