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 ...

In this paper, we are interested in a special class of integer matrices, namely the power-product matrix, defined with two positive integers n and d. Each matrix element is computed by weak compositions d into parts. The has several interesting applications such as power-sum representation polynomials difference-of-convex-sums-of-squares decomposition polynomials. We investigate some properties...

harmonics have become an important issue in modern power systems. the widespread penetration of non-linear loads to emerging power systems has turned power quality analysis into an important operation issue under both steady state and transient conditions. this paper employs an extended harmonic domain (ehd) based framework for dynamic analysis of long term analysis over voltages during the tra...