A recursive relation for Bell polynomials of arbitrary order is given. Such a result is useful, in that it allows us to define a Bell polynomial of order α ∈ R without resorting to more complicated constructions, such as fractional calculus, or other methods employed in the literature. One drawback is that the recursive definition requires infinite many terms when α / ∈ R. are defined as B n (x...

Data in many real-life engineering and economical problems suffer from inexactness. Herein we assume that we are given some intervals in which the data can simultaneously and independently perturb. We consider a generalized linear fractional programming problem with interval data and present an efficient method for computing the range of optimal values. The method reduces the problem to solving...

The capability calculus is a framework for statically reasoning about program resources such as deallocatable memory regions. Fractional capabilities, originally proposed by Boyland for checking the determinism of parallel reads in multi-thread programs, extend the capability calculus by extending the capabilities to range over the rational numbers. Fractional capabilities have since found nume...

Abstract In this paper a new method to compute approximate analytical solutions for differential equations of fractional order is presented. The proposed computational method, called the Piecewise Polynomial Least Squares Method (PWPLSM), combination and piecewise-defined functions. Numerical results different orders are discussed. obtained with PWPLSM compared other existing numerical solution...

In this paper, we study a class of fractional semi-infinite polynomial programming (FSIPP) problems, in which the objective is fraction convex and concave polynomial, constraints consist infinitely many inequalities. To solve such problem, first reformulate it to pair primal dual conic optimization reduce semidefinite (SDP) problems if can bring sum-of-squares structures into constraints. end, ...

In this paper, we develop necessary conditions for global optimality that apply to non-linear programming problems with polynomial constraints which cover a broad range of optimization problems that arise in applications of continuous as well as discrete optimization. In particular, we show that our optimality conditions readily apply to problems where the objective function is the difference o...