Discussion on the Leibniz rule and Laplace transform of fractional derivatives using series representation

DOI10.1080/10652469.2019.1694923zbMath1436.26008arXiv1901.11138OpenAlexW2991281091WikidataQ123257790 ScholiaQ123257790MaRDI QIDQ5217263

Da-Yan Liu, Yong Wang, Yiheng Wei, Peter W. Tse

Publication date: 24 February 2020

Published in: Integral Transforms and Special Functions (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1901.11138

zbMATH Keywords

Laplace transformTaylor seriesfractional calculusLeibniz rulenon-zero initial instant

Mathematics Subject Classification ID

Fractional derivatives and integrals (26A33) Numerical methods for initial value problems involving ordinary differential equations (65L05) Laplace transform (44A10) Universal Taylor series in one complex variable (30K05)

Related Items (1)

Generalized fractional Cauchy-Riemann operator associated with the fractional Cauchy-Riemann operator

Cites Work

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• What is a fractional derivative?
• Non-asymptotic fractional order differentiator for a class of fractional order linear systems
• No violation of the Leibniz rule. No fractional derivative
• The analysis of fractional differential equations. An application-oriented exposition using differential operators of Caputo type
• The fractional calculus. Theory and applications of differentiation and integration to arbitrary order
• Fractional differential equations. An introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications
• A note on short memory principle of fractional calculus
• Parameters and fractional differentiation orders estimation for linear continuous-time non-commensurate fractional order systems
• Lyapunov functions for Riemann-Liouville-like fractional difference equations
• Some properties of pseudo-fractional operators
• On the series representation of nabla discrete fractional calculus
• A new glance on the Leibniz rule for fractional derivatives
• A new collection of real world applications of fractional calculus in science and engineering
• A review of definitions of fractional derivatives and other operators
• Comments on ``Fractional order Lyapunov stability theorem and its applications in synchronization of complex dynamical networks
• Lyapunov functions for fractional order systems
• Fractional order Lyapunov stability theorem and its applications in synchronization of complex dynamical networks
• Fractional order chattering-free robust adaptive backstepping control technique
• Fractional calculus on time scales with Taylor's theorem
• Integral representation of solutions of fractional system with distributed delays
• Elasticity for economic processes with memory: fractional differential calculus approach
• The convolution method for the development of new leibniz rules involving fractional derivatives and of their integral analogues
• A new Leibniz rule and its integral analogue for fractional derivatives
• The application of a generalized leibniz rule to infinite sums
• Tomorrow’s Dynamics
• The Fractional Derivative of a Composite Function
• Fractional Derivatives and Leibniz Rule
• The Integral Analog of the Leibniz Rule

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