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 ...

Fractional differential equations have been of great interest recently. This is because of both the intensive development of the theory of fractional calculus itself and the applications of such constructions in various scientific fields such as physics, mechanics, chemistry, engineering, etc. Differential equations with impulsive effects arising from the real world describe the dyn...

Abstract The research of a formulation to model non-local interactions in the mechanical behavior matter is currently an open problem. In this context, strong based on fractional calculus provided paper. This derived from analogy with long-memory viscoelastic models. Specifically, same kind power-law time-dependent kernel used Boltzmann integral stress-strain relation as Fredholm relation. lead...

The aim of this paper is to present a new numerical method for solving the Bagley-Torvik equation. This equation has an important role in fractional calculus. The fractional derivatives are described based on the Caputo sense. Some properties of the sinc functions required for our subsequent development are given and are utilized to reduce the computation of solution of the Bagley-Torvik equati...

This paper deals with the design fractional solution of Bessel equation. We obtain explicit solutions of the equation with the help of fractional calculus techniques. Using the N-fractional calculus operator N(ν) method, we derive the fractional solutions of the equation.

With the rapid development of fractional calculus and active control techniques, stability of fractional-delay systems has been an increasing interest in engineering applications. For the local stability of an equilibrium of a linear dynamical system, the integral form of Mihkailov’s criterion, Nyquist criterion, and Stepan-Hassard’s criterion are probably among the most effective criteria. Thi...