Modified Riemann-Liouville derivative and fractional Taylor series of nondifferentiable functions further results

By Guy Jumarie. Computers and Mathematics with Applications, 2006

1,137 citations recorded by the source corpus.

Subfields: Modeling and Simulation, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/50594566fc728e7d7e7f40e367fc449818c0a730

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Modeling and Simulation

In Statistical and Nonlinear Physics

Citations in the corpus

An Extended Fractional Complex Transform (2010, background): “y o, ta\ where ζΛ ' is a modified Riemann-Liouville derivative defined as [2] o Dxm= 1 d" T(n-a)dx * where jce[0, l ] , n - \ < a < η and n > 1.”
The Use of Fractional Order Derivative to Predict the Groundwater Flow (2013, background): “Caputo derivatives are defined only for differentiable functions while functions that have no first-order derivative might have fractional derivatives of all orders less than one in the RiemannLiouville sense [12, 13].”
On chain rule for fractional derivatives (2016, background): “For example, the chain rule, which is suggested in [11–16], has the form D x f (g(x)) = ( D g f (g) ) g=g(x)D α x g(x), (3)”
Leibniz rule and fractional derivatives of power functions (2016, neutral): “[20–40].”
Extension of Matched Asymptotic Method to Fractional Boundary Layers Problems (2014, background): “Some Definitions of Fractional Derivatives There exist a quite few definitions of fractional derivatives in the literature; we will present the definition of a few [7–12].”
A fractional calculus of variations for multiple integrals with application to vibrating string (2010, methodology): “For that we make use of the recent Jumarie fractional integral and derivative [24, 25, 28], extending such notions to the multidimensional case.”
Counterexamples on Jumarie's three basic fractional calculus formulae for non-differentiable continuous functions (2016, background): “1 Introduction Jumarie proposed a modified Riemann-Liouville fractional derivative[1-5]: f (t) = 1 Γ(1− α) d dt ∫ t”
A note on exp-function method combined with complex transform method applied to fractional differential equations (2015, methodology): “Jumarie proposed a modi ed Riemann–Liouville derivative [28].”
Exact solutions of nonlinear time fractional partial differential equations by sub‐equation method (2015, methodology): “In [19], Jumarie proposed a modified Riemann–Liouville derivative.”