Leibniz-type rule of variable-order fractional derivative and application to build Lie symmetry framework

DOI10.1016/j.amc.2022.127268OpenAlexW4281289572WikidataQ114210844 ScholiaQ114210844MaRDI QIDQ2148035

Cheng-Bao Liu, Zhi Yong Zhang

Publication date: 21 June 2022

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.amc.2022.127268

zbMATH Keywords

reductionsymmetry structurevariable-order fractional derivativeLeibniz-type ruleLie symmetry framework

Mathematics Subject Classification ID

Functions of one variable (26Axx) Miscellaneous topics in partial differential equations (35Rxx) General theory for ordinary differential equations (34Axx)

Cites Work

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• What is a fractional derivative?
• A foundational approach to the Lie theory for fractional order partial differential equations
• Symmetries and conservation laws of partial differential equations: Basic notions and results
• Applications of symmetry methods to partial differential equations
• Variable order differential equations with piecewise constant order-function and diffusion with changing modes
• The fractional calculus. Theory and applications of differentiation and integration to arbitrary order
• Invariance of a partial differential equation of fractional order under the Lie group of scaling transformations
• Analytical solution of fractional variable order differential equations
• Symmetries and exact solutions of the time fractional Harry-Dym equation with Riemann-Liouville derivative
• Variable order and distributed order fractional operators
• Majorana representation for a composite system
• Symmetry analysis of initial and boundary value problems for fractional differential equations in Caputo sense
• A note on function space and boundedness of the general fractional integral in continuous time random walk
• A new collection of real world applications of fractional calculus in science and engineering
• On the variable order dynamics of the nonlinear wake caused by a sedimenting particle
• A review on variable-order fractional differential equations: mathematical foundations, physical models, numerical methods and applications
• Fractional Partial Differential Equations and Their Numerical Solutions
• Mechanics with variable-order differential operators
• Integration and differentiation to a variable fractional order
• Symmetry structure of multi-dimensional time-fractional partial differential equations
• Local symmetry structure and potential symmetries of time‐fractional partial differential equations
• Applications of variable-order fractional operators: a review
• Symmetry determination and nonlinearization of a nonlinear time-fractional partial differential equation
• Leibniz Rule for Fractional Derivatives Generalized and an Application to Infinite Series
• Fractional diffusion in inhomogeneous media
• The random walk's guide to anomalous diffusion: A fractional dynamics approach