in recent years, there has been greater attempt to find numerical solutions of differential equations using wavelet's methods. the following method is based on vector forms of haar-wavelet functions. in this paper, we will introduce one dimensional haar-wavelet functions and the haar-wavelet operational matrices of the fractional order integration. also the haar-wavelet operational matrice...

We live in an era when a remarkable number of new information and other technologies are successfully bypassing the main obstacle to technological advance: technology support network (TSN). Technology support net, when fully established and fixed, erects significant barriers to innovation. Innovation is not free and autonomous process of applied creativity, but is technically, economically and ...

in this paper, we develop an efficient legendre wavelets collocation method for well known time-fractional heat equation. inthe proposed method, we apply operational matrix of fractionalintegration to obtain numerical solution of the inhomogeneoustime-fractional heat equation with lateral heat loss and dirichletboundary conditions. the power of this manageable method isconfirmed. moreover, the ...

The plasmasphere is a region of cold and dense plasma around the Earth, corotating with Earth. Its density very dynamic under influence solar wind it influences several processes such as GPS navigation, surface charging satellites propagation growth waves. In this manuscript, we present new machine-learning model equatorial depending only on Kp index solar-wind properties at L1 Lagrange point. ...

This paper briefly describes a technique for improving capacity and operational stability of busy mainline junctions and stations. The technique, called the SafeCap advisory system, employs a mixture of existing train monitoring and control technologies to introduce an advisory control layer on top of fixed-block signalling. We present the main design principles and illustrate the advantages of...