A new Definition of Fractional Derivative without Singular Kernel

By Michele Caputo, Mauro Fabrizio. 2015

3,220 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/c2d54cab20e4940cb188f89cd4c7f8cfed753063

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Citations in the corpus

Stability Analysis of a Fractional-Order Linear System Described by the Caputo–Fabrizio Derivative (2019, background): “Recently, a new definition of the fractional derivative without a singular kernel has been proposed by Caputo and Fabrizio in 2015 [15].”
A powerful approach for fractional Drinfeld–Sokolov–Wilson equation with Mittag-Leffler law (2019, background): “Later, in 2015 Caputo and Fabrizio defeated the above obliges [45], and many researchers are considered this derivative in order to analyse and find the solution for diverse classes of nonlinear complex problems.”
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].”
Properties of a New Fractional Derivative without Singular Kernel (2015, background): “Suppose that the initial value problem ( 5)-(6) has two solutions, f1 and f2.”
On some new properties of fractional derivatives with Mittag-Leffler kernel (2017, unknown): “Recently, Caputo and Fabrizio [14] have proposed a new definition of fractional derivatives: CFDαc+f(x) ≔ M(α) 1−α d dt ∫ x c exp [ −α 1−α (x− y) ] f(y) dy, valid for 0 α 1, with M(α) being a normalisation function satisfying M(0) = M(1) = 1.”
On more general forms of proportional fractional operators (2019, background): “For such types of fractional operators we refer to [16, 17, 18, 19, 20].”
A NEW FRACTIONAL DERIVATIVE WITHOUT SINGULAR KERNEL Application to the Modelling of the Steady Heat Flow (2015, methodology): “x λ λ ψ ψ Π = − − With the help of the following approximation to the identity [9, 13]:”
Fractional Calculus involving (p, q)-Mathieu Type Series (2020, background): “Kumar et al. [21] ISSN 2444-8656 doi:10.2478/AMNS.2020.2.00011 analyzed the fractional model of modified Kawahara equation by using newly introduced Caputo-Fabrizio fractional derivative.”