In this paper, a new numerical method for solving fractional optimal control problems (FOCPs) is presented. The fractional derivative in the dynamic system is described in the Caputo sense. The method is based upon biorthogonal cubic Hermite spline multiwavelets approximations. The properties of biorthogonal multiwavelets are first given. The operational matrix of fractional Riemann-Lioville in...

let $r$ be a commutative ring. in this paper, by using algebraic properties of $r$, we study the hase digraph of prime ideals of $r$.

in this paper we investigate the algebraic properties of dimension of fuzzy hypervector spaces. also, we prove that two isomorphic fuzzy hypervector spaces have the same dimension.

In this paper, biochemical reaction problem is given in the form of a system of non-linear differential equations involving Caputo fractional derivative. The aim is to suggest an instrumental scheme to approximate the solution of this problem. To achieve this goal, the fractional derivation terms are expanded as the elements of shifted Legendre scaling functions. Then, applying operational matr...

The principal aim of this paper is to serve the numerical solution of an integral-algebraic equation (IAE) by using the Bernoulli polynomials and the residual correction method. After implementation of our scheme, the main problem would be transformed into a system of algebraic equations such that its solutions are the unknown Bernoulli coefficients. This method gives an analytic solution when ...

Following the categorical approach to universal algebra through algebraic theories, proposed by F.~W.~Lawvere in his PhD thesis, this paper aims at introducing a similar setting for general topology. The cornerstone of the new framework is the notion of emph{categorically-algebraic} (emph{catalg}) emph{topological theory}, whose models induce a category of topological structures. We introduce t...

in this paper, the time-like hyperruled surfaces in the minkowski 4-space and their algebraicinvariants are worked. also some characteristic results are found about these algebraic invariants.