مشتق ریمان-لیوویل اصلاح شده(جوماری)؛ مزایا و معایب

[1] U. Ghosh, J. Banerjee, S. Sarkar and S. Das, Fractional Klein–Gordon equation composed of Jumarie fractional derivative and its interpretation by a smoothness parameter, Pramana - J Phys, 90 (2018).
[2] G. Jumarie, Stochastic differential equations with fractional Brownian motion input, Internat. J. Systems Sci., 24 (1993) 1113–1131.
[3] G. Jumarie, Modified Riemann-Liouville derivative and fractional Taylor series of nondifferentiable functions further results, Comput. Math. Appl., 51 (2006) 1367–1376.
[4] G. Jumarie, Table of some basic fractional calculus formulae derived from a modified Riemann-Liouville derivative for non-differentiable functions, Appl. Math. Lett., 22 (2009) 378–385.
[5] G. Jumarie, The Leibniz rule for fractional derivatives holds with non-differentiable functions, Math. Stat.,1 (2013) 50–52.
[6] C. S. Liu, Counterexamples on Jumarie’s two basic fractional calculus formulae, Commun. Nonlinear Sci. Numer. Simul., 22 (2015) 92–94.
[7] C. S. Liu, Counterexamples on Jumarie’s three basic fractional calculus formulae for non-differentiable continuous functions, Chaos Solitons Fractals, 109 (2018) 219-222.
[8] K. Oldham and J. Spanier, The fractional calculus theory and applications of differentiation and integration to arbitrary order, Elsevier 1974.
[9] I. Podlubny, Fractional differential equations, Academic Press, Inc., San Diego, CA, 1999.
[10] A new approach for the generalized fractional Casson fluid model with Newtonian heating described by the modified Riemann-Liouville fractional operator, Math. Methods Appl. Sci., 45 (2022) 3574–3588.