Stochastic Calculus for Fractional Brownian Motion I. Theory
SIAM Journal on Control and Optimization
Analytical approximate solutions for nonlinear fractional differential equations
Applied Mathematics and Computation
Systems Analysis Modelling Simulation
A fractional variational iteration method for solving fractional nonlinear differential equations
Computers & Mathematics with Applications
Analytical treatment of differential equations with fractional coordinate derivatives
Computers & Mathematics with Applications
Analytical modelling of fractional advection-dispersion equation defined in a bounded space domain
Mathematical and Computer Modelling: An International Journal
Derivation of an amplitude of information in the setting of a new family of fractional entropies
Information Sciences: an International Journal
New solutions for some time fractional differential equations
International Journal of Computing Science and Mathematics
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The paper gives some results and improves the derivation of the fractional Taylor's series of nondifferentiable functions obtained recently in the form f (@g + h) = E"@a (h^@aD"@g^@a)f(@g), 0 @a @? 1, where E"@a is the Mittag-Leffier function. Here, one defines fractional derivative as the limit of fractional difference, and by this way one can circumvent the problem which arises with the definition of the fractional derivative of constant using Riemann-Liouville definition. As a result, a modified Riemann-Liouville definition is proposed, which is fully consistent with the fractional difference definition and avoids any reference to the derivative of order greater than the considered one's. In order to support this F-Taylor series, one shows how its first term can be obtained directly in the form of a mean value formula. The fractional derivative of the Dirac delta function is obtained together with the fractional Taylor's series of multivariate functions. The relation with irreversibility of time and symmetry breaking is exhibited, and to some extent, this F-Taylor's series generalizes the fractional mean value formula obtained a few years ago by Kolwantar.