Table of some basic fractional calculus formulae derived from a modified Riemann-Liouville derivative for non-differentiable functions

By Guy Jumarie. Applied Mathematics Letters, 2009

521 citations recorded by the source corpus.

Subfields: Mathematical Physics, Modeling and Simulation, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/969b2bc13e630bd1fdb58513fb3b6ddea0a8370a

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Citations in the corpus

On chain rule for fractional derivatives (2016, background): “4 of [15], Eq.”
Fractional Complex Transform and exp-Function Methods for Fractional Differential Equations (2013, methodology): “the Riemann-Liouville derivative [22], Jumarie’s modified Riemann-Liouville derivative [23, 24].”
Multiple positive solutions for (n-1, 1)-type semipositone conjugate boundary value problems of nonlinear fractional differential equations (2010, background): “Because of fractional differential equation’s modeling capabilities in engineering, science, economy, and other fields, the last few decades has resulted in a rapid development of the theory of fractional differential equation; see [1]-[7] for a good overview.”
A note on exp-function method combined with complex transform method applied to fractional differential equations (2015, background): “Then Jumarie’s modi ed Riemann–Liouville derivative of order α is de ned by the expression ([29])”
Control of a novel class of fractional-order chaotic systems via adaptive sliding mode control approach ☆ (2013, background): “Introduction In the past few decades, much attention has been drawn for the study of fractional calculus [1–7].”
An Extended Fractional Complex Transform (2010, methodology): “We introduce some useful properties of the modified Riemann-Liouville derivative [3-5]:”
The Modified Trial Equation Method for Fractional Wave Equation and Time Fractional Generalized Burgers Equation (2013, methodology): “We consider time fractional generalized Burgers equation [27] described as follows:”
Exact solutions of nonlinear time fractional partial differential equations by sub‐equation method (2015, background): “Thus, the fractional derivatives can be defined as follows [19, 23].”
Two positive solutions for (n − 1, 1)-type semipositone integral boundary value problems for coupled systems of nonlinear fractional differential equations☆ (2012, background): “Because of fractional differential equation’s modeling capabilities in engineering, science, economics, and other fields, the last few decades has resulted in a rapid development of the theory of fractional differential equations, see [1]-[7] for a good overview.”
Fractal solids, product measures and fractional wave equations (2009, methodology): “In the sequel, adopting a modified Riemann–Liouville fractional integral recently formulated by Jumarie (2005, 2008), we have Proc.”
A fractional calculus of variations for multiple integrals with application to vibrating string (2010, methodology): “The following equalities can be considered as fractional counterparts of the first and the second fundamental theorems of calculus and can be found in [27, 28]: d dxα ∫ x”