A review of definitions of fractional derivatives and other operators
GS Teodoro, JAT Machado, EC De Oliveira - Journal of Computational …, 2019 - Elsevier
Given the increasing number of proposals and definitions of operators in the scope of
fractional calculus, it is important to introduce a systematic classification. Nonetheless, many …
fractional calculus, it is important to introduce a systematic classification. Nonetheless, many …
Conformable Laplace transform of fractional differential equations
In this paper, we use the conformable fractional derivative to discuss some fractional linear
differential equations with constant coefficients. By applying some similar arguments to the …
differential equations with constant coefficients. By applying some similar arguments to the …
A critical analysis of the conformable derivative
AA Abdelhakim, JAT Machado - Nonlinear Dynamics, 2019 - Springer
We prove that conformable “fractional” differentiability of a function f: 0, ∞\, ⟶ R f: 0,∞⟶ R is
nothing else than the classical differentiability. More precisely, the conformable α α …
nothing else than the classical differentiability. More precisely, the conformable α α …
[HTML][HTML] Stability analysis of conformable fractional-order nonlinear systems
Stability analysis of conformable fractional-order nonlinear systems - ScienceDirect Skip to main
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Controllability, observability and fractional linear-quadratic problem for fractional linear systems with conformable fractional derivatives and some applications
In the present paper, we investigate the controllability, observability and fractional linear-
quadratic problem of a non-homogeneous continuous-time fractional dynamical system (CF …
quadratic problem of a non-homogeneous continuous-time fractional dynamical system (CF …
On the averaging principle for stochastic differential equations involving Caputo fractional derivative
G Xiao, M Fečkan, JR Wang - Chaos: An Interdisciplinary Journal of …, 2022 - pubs.aip.org
In this paper, we investigate the averaging principle for Caputo-type fractional stochastic
differential equations driven by Brownian motion. Different from the approach of integration …
differential equations driven by Brownian motion. Different from the approach of integration …
[PDF][PDF] On the nature of the conformable derivative and its applications to physics
The purpose of this work is to show that the Khalil and Katagampoula conformable
derivatives are equivalent to the simple change of variables x→ xα/α, where α is the order of …
derivatives are equivalent to the simple change of variables x→ xα/α, where α is the order of …
Variational calculus with conformable fractional derivatives
MJ Lazo, DFM Torres - IEEE/CAA Journal of automatica sinica, 2016 - ieeexplore.ieee.org
Invariant conditions for conformable fractional problems of the calculus of variations under
the presence of external forces in the dynamics are studied. Depending on the type of …
the presence of external forces in the dynamics are studied. Depending on the type of …
Solving Helmholtz equation with local fractional derivative operators
The paper presents a new analytical method called the local fractional Laplace variational
iteration method (LFLVIM), which is a combination of the local fractional Laplace transform …
iteration method (LFLVIM), which is a combination of the local fractional Laplace transform …
Analytical solutions of (2+ time fractional order) dimensional physical models, using modified decomposition method
In this article, a new analytical technique based on an innovative transformation is used to
solve (2+ time fractional-order) dimensional physical models. The proposed method is the …
solve (2+ time fractional-order) dimensional physical models. The proposed method is the …