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

Pointing out that Λ-fractional analysis is the unique fractional calculus theory including mathematically acceptable derivatives, variational for established. Since a non-local procedure, global extremals are only accepted. That means should satisfy not Euler–Lagrange equation but also additional Weierstrass-Erdmann corner conditions. Hence stability criteria introduced. The proposed procedure ...

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...