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In this paper we present an extension of the non-conformable local fractional derivative, to the case of functions of severalvariables. Results analogous to those known from the classic multivariatecalculus are presented. To show the strength of this approach, we show anextension of the Second Lyapunov Method to the non-conformable localfractional case.
Content available remote Non-local Kirchhoff–Love plates in terms of fractional calculus
Modern continuum mechanics needs new mathematical techniques to describe the complexity of real physical processes. Recently fractional calculus, a branch of mathematical analysis that studies differential operators of an arbitrary (real or complex) order, emerged as a powerful tool for modelling complex systems. It is due to the fact that fractional differential operators introduce non-locality to the description considered in a natural way. In this sense they generalize classical (local) formulations and make the description more realistic. This paper deals with the generalisation of the Kirchhoff–Love plates theory using fractional calculus. This new formulation in non-local, thus all common fields like e.g. internal forces or displacements at a specific point contain somehow information from its finite surroundings, which is in agreement with experimental observations.
Content available remote Filippov Lemma for certain differential inclusion of third order
We propose a version of the Filippov Lemma for differential inclusions of the type y'" + k2y' is an element of F(x,y) defined on [—1,1] with boundary conditions y(-1)=y(1)=y'(1)=0.
Content available remote On an operatorial inequality
In this paper we give an operatorial inequality which is applied to find estimations for the solutions of some integral and differential systems of inequalities.
In the present paper, making use of certain operators, some theorems involving inequalities on meromorphically multivalent functions in the punctured unit disk are obtained. Moreover, some of the results which are important for geometric function theory are also included.
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