We study the long time behavior of a Brownian particle moving in an anomalously diffusing field, the evolution of which depends on the particle position. We prove that the process describing the asymptotic behavior of the Brownian particle has bounded (in time) variance when the particle interacts with a subdiffusive field; when the interaction is with a superdiffusive field the variance of the...

Although there have existed some numerical algorithms for the fractional differential equations, developing high-order methods (i.e., with convergence order greater than or equal to 2) is just the beginning. Lubich has ever proposed the high-order schemes when he studied the fractional linear multistep methods, where he constructed the pth order schemes (p = 2, 3, 4, 5, 6) for the αth order Rie...

Discrete maps with long-term memory are obtained from nonlinear differential equations with Riemann–Liouville and Caputo fractional derivatives. These maps are generalizations of the well-known universal map. The memory means that their present state is determined by all past states with special forms of weights. To obtain discrete maps from fractional differential equations, we use the equival...

In this paper, we use the Riemann-Liouville fractionalintegrals to establish some new integral inequalities related toChebyshev's functional in the case of two differentiable functions.

The current study presents a comprehensive Lie symmetry analysis for the time-fractional Mikhailov–Novikov–Wang (MNW) system with Riemann–Liouville fractional derivative. corresponding simplified equations Erdélyi–Kober derivative are constructed by group invariant solutions. Furthermore, we obtain explicit solutions help of power series method and show dynamical behavior via evolutional figure...

In this paper, we present recent results in integral inequality theory. Our results are based on thefractional integration in the sense of Riemann-Liouville

in this paper, we present recent results in integral inequality theory. our results are based on thefractional integration in the sense of riemann-liouville