Properties of a New Fractional Derivative without Singular Kernel

By Jorge Losada, J. J. Nieto, Saudi Arabia. 2015

943 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/b962ca954739e9115f80b76452d0fe19c10e8efb

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

Citations in the corpus

A numerical approach for solving fractional optimal control problems with mittag-leffler kernel (2021, background): “Hence, many authors have introduced several definitions for fractional integral and derivative operators with the nonlocal and non-singular kernel such as Caputo–Fabrizio (CF) (Caputo and Fabrizio, 2015); Losada and Nieto, 2015) and Atangana–Baleanu (Atangana and Baleanu, 2016).”
Hyers–Ulam Stability and Existence of Solutions for Differential Equations with Caputo–Fabrizio Fractional Derivative (2019, methodology): “Losada and Nieto [22] presented a fractional integral corresponding to the Caputo–Fabrizio fractional derivative and introduced Caputo–Fabrizio fractional differential equations and established existence and uniqueness results.”
Arbitrary Order Fractional Difference Operators with Discrete Exponential Kernels and Applications (2017, background): “More properties of this fractional derivative have been studied in [9], where the correspondent fractional integral operatorwas formulated.”
Three-Point Boundary Value Problems for Conformable Fractional Differential Equations (2015, background): “There are several concepts of fractional derivatives, some classical, such as RiemannLiouville or Caputo definitions, and some novel, such as conformable fractional derivative [1], β-derivative [2], or a new definition [3, 4].”
Numerical solution for the model of RLC circuit via the fractional derivative without singular kernel (2015, methodology): “M a ð Þ= 2 2 a , 0\a\1 Without any doubt, this new derivative will be used in all the branches of sciences for modeling.(8) In order to translate from ordinary differential equations to fractional differential equations, we present the following mathematical transition for the time and space compone”
On Coupled Systems of Time-Fractional Differential Problems by Using a New Fractional Derivative (2016, background): “where 0 < α < 1 and (x, t) ∈ [0, 1] × [0, 1] [11].”
A new fractional operator of variable order: Application in the description of anomalous diffusion (2016, methodology): “r2016 of the AD was reported in [10], and the AD equation with a generalized FOD of Riemann–Liouville type was proposed in [11]. POD using the function kernel of the exponential type were reported in [12,13,14,15]. The applications of the FOD to model the surface of shallow water (SSW) [16], heat tr”