Certain Analytic Formulas Linked to Locally Fractional Differential and Integral Operators
Journal of Function Spaces, 2022 The present investigation is aimed at defining different classes of analytic functions and conformable differential operators in view of the concept of locally fractional differential and integral operators. We present a novel generalized class of analytic functions, which we call it locally fractional analytic functions in the open unit disk.
Ibtisam Aldawish, Rabha W. Ibrahim
openaire +3 more sources
Some Generalized Steffensen’s Inequalities via a New Identity for Local Fractional Integrals
International Journal of Analysis and Applications, 2017 In this study, we first give an identity for local fractional integrals. We then make use of this identity in order to derive several generalizations of the celebrated Steffensen’s inequality associated with local fractional integrals.
Tuba Tunç +2 more
doaj +2 more sources
A Class of Quasilinear Equations with Distributed Gerasimov–Caputo Derivatives
Mathematics, 2023 Quasilinear equations in Banach spaces with distributed Gerasimov–Caputo fractional derivatives, which are defined by the Riemann–Stieltjes integrals, and with a linear closed operator A, are studied.
Vladimir E. Fedorov, Nikolay V. Filin
doaj +1 more source
Fractional Gradient Elasticity from Spatial Dispersion Law [PDF]
, 2014 Non-local elasticity models in continuum mechanics can be treated with two different approaches: the gradient elasticity models (weak non-locality) and the integral non-local models (strong non-locality).
Tarasov, Vasily E.
core +3 more sources
A matrix approach to multi-term fractional differential equations using two new diffusive representations for the Caputo fractional derivative [PDF]
AUT Journal of Mathematics and ComputingIn the last decade, there has been a surge of interest in application of fractional calculus in various areas such as, mathematics, physics, engineering, mechanics and etc.
Hassan Khosravian-Arab, Mehdi Dehghan
doaj +1 more source
A tree approach to $p$-variation and to integration [PDF]
, 2008 We consider a real-valued path; it is possible to associate a tree to this path, and we explore the relations between the tree, the properties of $p$-variation of the path, and integration with respect to the path. In particular, the fractal dimension of
Picard, Jean
core +8 more sources
Fractional-Spin Integrals of Motion for the Boundary Sine-Gordon Model at the Free Fermion Point [PDF]
, 1997 We construct integrals of motion (IM) for the sine-Gordon model with boundary at the free Fermion point which correctly determine the boundary S matrix.
Coleman S. +4 more
core +2 more sources
Local Truncation Error of Low-Order Fractional Variational Integrators [PDF]
, 2019 We study the local truncation error of the so-called fractional variational integrators, recently developed in [1, 2] based on previous work by Riewe and Cresson [3, 4]. These integrators are obtained through two main elements: the enlarging of the usual mechanical Lagrangian state space by the introduction of the fractional derivatives of the ...
Jiménez, F, Ober-Blöbaum, S
openaire +1 more source
Advances in Difference Equations, 2020 The concept of generalized h-preinvex function on real linear fractal sets R β $R^{\beta }$ ( 0 < β ≤ 1 $0 < \beta \le 1$ ) is introduced, which extends generalized preinvex, generalized s-preinvex, generalized Godunova–Levin preinvex, and generalized P ...
Wenbing Sun
doaj +1 more source
Possible Experimental Test of Continuous Medium Model for Fractal Media
, 2005 We use the fractional integrals to describe fractal media. We consider the fractal media as special ("fractional") continuous media. We discuss the possible experimental testing of the continuous medium model for fractal media that is suggested in Phys ...
Avnir +22 more
core +2 more sources