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Towards a non-conformable fractional calculus of n-variables

Martínez Francisco, Nápoles Juan E. Valdés

Journal of Mathematics and Applications

2020

Vol. 43

87--98

In this paper we present an extension of the non-conformable local fractional derivative, to the case of functions of several variables. Results analogous to those known from the classic multivariate calculus are presented. To show the strength of this approach, we show an extension of the Second Lyapunov Method to the non-conformable local fractional case.

Non-local Kirchhoff–Love plates in terms of fractional calculus

Sumelka W.

Archives of Civil and Mechanical Engineering

2015

Vol. 15, no. 1

231--242

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.

Filippov Lemma for certain differential inclusion of third order

Bartuzel G., Fryszkowski A.

Demonstratio Mathematica

2008

Vol. 41, nr 2

337-352

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.

On an operatorial inequality

Popa V., Lungu N.

Demonstratio Mathematica

2005

Vol. 38, nr 3

667-674

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.

Certain operators and inequalities and their applications to meromorphically multivalent functions

Dziok J., Irmak H.

Demonstratio Mathematica

2003

Vol. 36, nr 4

839--846

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.