The object of this paper is to establish certain generalized fractional integration and differentiation involving generalized Mittag-Leffler function defined by Salim and Faraj [25]. The considered generalized fractional calculus operators contain the Appell's function $F_3$ [2, p.224] as kernel and are introduced by Saigo and Maeda [23]. The Marichev-Saigo-Maeda fractional calculus operators a...

In this article we investigate some modifications of the total variation inpainting model and discuss the existence as well as the smoothness of solutions to these new variational problems. We emphasize that our variant of a linear growth regulariza-tion is completely discussed in the Sobolev space W 1 1 without passing to a relaxed version in the space of functions with bounded variation.

The Euler-Lagrange equation plays an important role in the minimization problems of the calculus of variations. This paper employs the differential transformation method (DTM) for finding the solution of the Euler-Lagrange equation which arise from problems of calculus of variations. DTM provides an analytical solution in the form of an infinite power series with easily computable components. S...

We prove that the Ciarlet-Nečas non-interpenetration of matter condition [9] can be extended to the case of SBV -deformations of hyperelastic brittle materials, and can be taken into account for some variational models in fracture mechanics. In order to formulate such a condition, we define the deformed configuration under an SBV -map by means of the approximately differentiable representative,...

Background: Enterococci are important gram-positive bacteria causing dental calculus in human beings; however, the role of these bacteria in oral cavity is unclear. The aim of this study was to investigate the presence of Enterococcal Surface Protein (esp) gene in Enterococcus faecalis isolated from dental calculus in the city of Sari, Iran. Materials and Methods: In the present study, 207 den...

we propose a method for medical image denoising using calculus of variations and local variance estimation by shaped windows. this method reduces any additive noise and preserves small patterns and edges of images. a pyramid structure-texture decomposition of images is used to separate noise and texture components based on local variance measures. the experimental results show that the proposed...

we describe a variational problem on a surface under a constraintof geometrical character. necessary and sufficient conditions for the existence ofbifurcation points are provided. in local coordinates the problem corresponds toa quasilinear elliptic boundary value problem. the problem can be consideredas a physical model for several applications referring to continuum medium andmembranes.

the object of this paper is to establish certain generalized fractional integration and differentiation involving generalized mittag-leffler function defined by salim and faraj [25]. the considered generalized fractional calculus operators contain the appell's function $f_3$ [2, p.224] as kernel and are introduced by saigo and maeda [23]. the marichev-saigo-maeda fractional calculus operat...

The calculus of variations addresses the need to optimize certain quantities over sets of functions. We begin by defining the notion of a functional and its role in performing calculus on variations of curves. In order to identify those functions which are extremals of a functional, we establish the first variation and the Euler-Lagrange Equations. A formulation of the second variation follows,...