On the generalized fractional derivatives and their Caputo modification

By Fahd Jarad, Thabet Abdeljawad, Dumitru Băleanu. 2017

272 citations recorded by the source corpus.

In this manuscript, we define the generalized fractional derivative on ACγ [a,b], the space of functions defined on [a,b] such that γn−1f ∈ AC[a,b], where γ = x1−ρ d dx . We present some of the properties of generalized fractional derivatives of these functions and then we define their Caputo version. c ©2017 All rights reserved.

Subfields: Applied Mathematics, Geometry and Topology, Modeling and Simulation

View Paper: https://www.semanticscholar.org/paper/44aaec5445ec98b96a8b0bffee4b9c768af9814e

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In Applied Mathematics

In Geometry and Topology

In Modeling and Simulation

Citations in the corpus

On a Caputo-type fractional derivative (2018, background): “[8] presented a new type of fractional operator, which recovers the Caputo and Caputo–Hadamard fractional derivatives.”
Generalized fractional derivatives and Laplace transform (2020, background): “After then, the corresponding derivatives are defined (see for example [20, 17, 18, 14, 12, 15, 16]).”
Existence and uniqueness of solutions to fractional differential equations in the frame of generalized Caputo fractional derivatives (2018, unknown): “For the functions in ACn γ [a, b] = {f : [a, b] → C and γ n–1f ∈ AC[a, b],γ = t1–ρ d dt } and Cn γ [a, b] = {f : [a, b] → C and γ n–1f ∈ C[a, b],γ = t1–ρ d dt }, the left and right generalized Caputo fractional derivatives of order α, (α) > 0 are given respectively as in [1] as follows:”
On generalized fractional operators and a gronwall type inequality with applications (2017, background): “[29] (i) Let α ∈ (0, 1] , β ≥ 0, 0 ≤ t0, ρ > 0.”
Analysis of some generalized ABC – Fractional logistic models (2019, background): “It can be realized that starting from the turn of this century researchers have proposed a variety of fractional operators [10, 11, 12, 13, 14, 15, 16] and added variety of fractional operators with different approaches to the field of fractional calculus.”