Finite differences, as a subclass of direct methods in the calculus of variations, consist in discretizing the objective functional using appropriate approximations for derivatives that appear in the problem. This article generalizes the same idea for fractional variational problems. We consider a minimization problem with a Lagrangian that depends on the left Riemann– Liouville fractional deri...

Finite differences, as a subclass of direct methods in the calculus of variations, consist in discretizing the objective functional using appropriate approximations for derivatives that appear in the problem. This article generalizes the same idea for fractional variational problems. We consider a minimization problem with a Lagrangian that depends only on the left Riemann–Liouville fractional ...

In this article, we develop the distributed order fractional hybrid differential equations (DOFHDEs) with linear perturbations involving the fractional Riemann-Liouville derivative of order $0 < q < 1$ with respect to a nonnegative density function. Furthermore, an existence theorem for the fractional hybrid differential equations of distributed order is proved under the mixed $varphi$-Lipschit...

in this paper, we use the riemann-liouville fractionalintegrals to establish some new integral inequalities related tochebyshev's functional in the case of two differentiable functions.

In this paper a new concept of duality is given for the linear fractional programming (LFP) problem in which the objective function is a linear fractional function and where the constraint functions are in the form of linear inequalities. Our result is based on transforming the linear fractional programming problem to an equivalent linear programming with the same dimension. A simple example is...

where An is the n-fold product of the σ-algebra A of subsets of a given set X , Fi, Gi, i∈ p ≡ {1,2, . . . , p}, and Hj , j ∈ q, are real-valued functions defined on An, and for each i∈ p, Gi(S) > 0 for all S∈An such that Hj(S) ≤ 0, j ∈ q. Optimization problems of this type in which the functions Fi, Gi, i∈ p, and Hj , j ∈ q, are defined on a subset of Rn (n-dimensional Euclidean space) are cal...

We show that SETF, the idealized version of the uniprocessor scheduling algorithm used by Unix, is scalable for the objective of fractional flow on a homogeneous multiprocessor. We also give a potential function analysis for the objective of weighted fractional flow on a uniprocessor.

The aim of the paper is to present sequential methods for a pseudoconvex optimization problem whose objective function is the sum of a linear and a linear fractional function and the feasible region is a polyhedron, not necessarily compact. Since the sum of a linear and a linear fractional function is not in general pseudoconvex, we first derive conditions characterizing its pseudoconvexity on ...

In this paper, we integrate goal programming (GP), Taylor Series, Kuhn-Tucker conditions and Penalty Function approaches to solve linear fractional bi-level programming (LFBLP)problems. As we know, the Taylor Series is having the property of transforming fractional functions to a polynomial. In the present article by Taylor Series we obtain polynomial objective functions which are equivalent to...

The main objective of this paper is to introduce k-fractional derivative operator by using the definition of k-beta function. We establish some results related to the newly defined fractional operator such as Mellin transform and relations to khypergeometric and k-Appell’s functions. Also, we investigate the k-fractional derivative of k-Mittag-Leffler and Wright hypergeometric functions.