The main aim of this article is to generalize the Legendre operational matrix to the fractional derivatives and implemented it to solve the nonlinear multi-order fractional differential equations. In this approach, a truncated Legendre series together with the Legendre operational matrix of fractional derivatives are used. The main characteristic behind the approach using this technique is that...

We develop the tau-spectral method to solve the time-fractional heat equation (T-FHE) with nonlocal condition. In order to achieve highly accurate solution of this problem, the operational matrix of fractional integration (described in the Riemann-Liouville sense) for shifted Legendre polynomials is investigated in conjunction with tau-spectral scheme and the Legendre operational polynomials ar...

Abstract This paper applies the Heydari–Hosseininia nonsingular fractional derivative for defining a variable-order version of Sobolev equation. The orthonormal shifted discrete Legendre polynomials, as an appropriate family basis functions, are employed to generate operational matrix method this A new related these polynomials is extracted and construct presented method. Using approach, algebr...

using monthly test day records the genetic parameters of iranian holstein cattle in first lactation were studied. data of 277400 test-day milk records from 65320 cows and 2210 sires were analyzed by an animal random regression model using restricted maximum likelihood methodology. the model included herd-test-date, interaction between year-season of calving, days in milk (linear and quadratic) ...

In this paper, summation formulae for the 2-variable Legendre polynomials in terms of certain multi-variable special polynomials are derived. Several summation formulae for the classical Legendre polynomials are also obtained as applications. Further, Hermite-Legendre polynomials are introduced and summation formulae for these polynomials are also established.

the low earth orbiting (leo) satellites are widely used for geosciences applications. for most applications, precise orbital information of the satellites is required. a combination of the in suite observations and dynamic orbit yields the optimum solution. in order to obtain the combined optimal solution, one needs to analytically or numerically propagate the state vector epoch by an epoch bas...

We determine the infinite sequences (ak) of integers that can be generated by polynomials with integral coefficients, in the sense that for each finite initial segment of length n there is an integral polynomial fn(x) of degree < n such that ak = fn(k) for k = 0, 1, . . . , n − 1. Let P be the set of such sequences and Π the additive group of all infinite sequences of integers. Then P is a subg...