A review of definitions of fractional derivatives and other operators
DOI10.1016/j.jcp.2019.03.008zbMath1452.26008OpenAlexW2922428687WikidataQ128200307 ScholiaQ128200307MaRDI QIDQ2220605
G. Sales Teodoro, Edmundo Capelas de Oliveira, José António Tenreiro Machado
Publication date: 25 January 2021
Published in: Journal of Computational Physics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.jcp.2019.03.008
fractional derivativesfractional calculusfractional operatorslocal operatorsoperators with nonsingular kernel
Differentiation (real functions of one variable): general theory, generalized derivatives, mean value theorems (26A24) Fractional derivatives and integrals (26A33) Research exposition (monographs, survey articles) pertaining to real functions (26-02)
Related Items
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Hilfer-Prabhakar derivatives and some applications
- Existence of solution to a local fractional nonlinear differential equation
- What is a fractional derivative?
- On Riesz-Caputo formulation for sequential fractional variational principles
- On a differential equation involving Hilfer-Hadamard fractional derivative
- On conformable fractional calculus
- Fractional Newton mechanics with conformable fractional derivative
- A remark on local fractional calculus and ordinary derivatives
- New approach to a generalized fractional integral
- On the new fractional derivative and application to nonlinear Fisher's reaction-diffusion equation
- The fractional quantum derivative and its integral representations
- Correction to ``What is a fractional derivative? by Ortigueira and Machado
- Riesz potential operators and inverses via fractional centred derivatives
- No violation of the Leibniz rule. No fractional derivative
- Counterexamples on Jumarie's two basic fractional calculus formulae
- Table of some basic fractional calculus formulae derived from a modified Riemann-Liouville derivative for non-differentiable functions
- Fractional derivatives in complex planes
- A coherent approach to non-integer order derivatives
- Hölder continuity and initial value problems of mixed type differential equations
- On the Ulam-Hyers-Rassias stability for nonlinear fractional differential equations using the \(\psi \)-Hilfer operator
- Relaxation and diffusion models with non-singular kernels
- Counterexamples on Jumarie's three basic fractional calculus formulae for non-differentiable continuous functions
- General conformable fractional derivative and its physical interpretation
- Mittag-Leffler functions and the truncated \(\mathcal {V}\)-fractional derivative
- Extension of matched asymptotic method to fractional boundary layers problems
- A review of definitions for fractional derivatives and integral
- A comment on some new definitions of fractional derivative
- Variable order and distributed order fractional operators
- Hilfer-Katugampola fractional derivatives
- A Caputo fractional derivative of a function with respect to another function
- On the formulation and numerical simulation of distributed-order fractional optimal control problems
- Representations of acting processes and memory effects: general fractional derivative and its application to theory of heat conduction with finite wave speeds
- Fractional conformable derivatives of Liouville-Caputo type with low-fractionality
- A critical analysis of the Caputo-Fabrizio operator
- Fractional and integer derivatives with continuously distributed lag
- Variable order fractional systems
- On the \(\psi\)-Hilfer fractional derivative
- A new definition of fractional derivative
- Implicit fractional differential equations via the Liouville-Caputo derivative
- Historical survey: the chronicles of fractional calculus
- Modified Riemann-Liouville derivative and fractional Taylor series of nondifferentiable. functions. Further results
- Time-space fabric underlying anomalous diffusion
- Some pioneers of the applications of fractional calculus
- Caputo–Hadamard Fractional Derivatives of Variable Order
- Two regularization methods for solving a Riesz–Feller space-fractional backward diffusion problem
- Fractional Central Differences and Derivatives
- Extended Riemann-Liouville fractional derivative operator and its applications
- On a Concept of Derivative of Complex Order with Applications to Special Functions
- The fundamental solution of the space-time fractional diffusion equation
- Fractional differentiability of nowhere differentiable functions and dimensions
- k-Hilfer-Prabhakar Fractional Derivatives and Applications
- A new truncated $M$-fractional derivative type unifying some fractional derivative types with classical properties
- The k-fractional Hilfer derivative