137 citations · 137 across the 1 of their papers we have counts for
5 papers
Trends, Directions for Further Research, and Some Open Problems of Fractional Calculus
Kai Diethelm, Virginia Kiryakova, Yuri Luchko +2
The area of fractional calculus (FC) has been fast developing and is presently being applied in all scientific fields. Therefore, it is of key relevance to assess the present state…
A critical analysis of the conformable derivative
Ahmed A. Abdelhakim, José A. Tenreiro Machado
We prove that conformable ``fractional" differentiability of a function is nothing else than the classical differentiability. More precis…
A new fractional derivative involving the normalized sinc function without singular kernel
Xiao-Jun Yang, Feng Gao, J. A. Tenreiro Machado +1
In this paper, a new fractional derivative involving the normalized sinc function without singular kernel is proposed. The Laplace transform is used to find the analytical solution…
A new fractional operator of variable order: application in the description of anomalous diffusion
Xiao-Jun Yang, J. A. Tenreiro Machado
In this paper, a new fractional operator of variable order with the use of the monotonic increasing function is proposed in sense of Caputo type. The properties in term of the Lapl…
A new fractional derivative without singular kernel: Application to the modelling of the steady heat flow
Xiao-Jun Yang, H. M. Srivastava, J. A. Tenreiro Machado
In this article we propose a new fractional derivative without singular kernel. We consider the potential application for modeling the steady heat-conduction problem. The analytica…