In recent years, fractional calculus has witnessed tremendous progress in various areas of sciences and mathematics [...]

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...

Abstract Fractional calculus was born in 1695 on September 30 due to a very deep question raised letter of L’Hospital Leibniz. The prophetical answer Leibniz that encapsulated huge inspiration for all generations scientists and is continuing stimulate the minds contemporary researchers. During 325 years existence, fractional has kept attention top level mathematicians, during last period time i...

We present a semilocal convergence study of Newton-type methods on a generalized Banach space setting to approximate a locally unique zero of an operator. Earlier studies require that the operator involved is Fréchet differentiable. In the present study we assume that the operator is only continuous. This way we extend the applicability of Newton-type methods to include fractional calculus and ...

Image denoising is an important task in image processing. The interest in using a fractional mask window operator based on fractional calculus has grown for image denoising. This paper mainly introduces the concept of fractional calculus and proposes a new mathematical method in using fractional Alexander polynomials for image denoising. The structures of n n fractional mask windows on eight di...

the aim of this work is to describe the qualitative behavior of the solution set of a givensystem of fractional differential equations and limiting behavior of the dynamical system or flow defined by the system of fractional differential equations. in order to achieve this goal, it is first necessary to develop the local theory for fractional nonlinear systems. this is done by the extension of ...