Results 61 to 70 of about 19,827 (284)

A Survey on Semilinear Differential Equations and Inclusions Involving Riemann-Liouville Fractional Derivative

, 2009
We establish sufficient conditions for the existence of mild solutions for some densely defined semilinear functional differential equations and inclusions involving the Riemann-Liouville fractional derivative.
R. Agarwal, M. Belmekki, M. Benchohra
semanticscholar   +1 more source

Stability Results for Implicit Fractional Pantograph Differential Equations via ϕ-Hilfer Fractional Derivative with a Nonlocal Riemann-Liouville Fractional Integral Condition

Mathematics, 2020
This paper presents a class of implicit pantograph fractional differential equation with more general Riemann-Liouville fractional integral condition. A certain class of generalized fractional derivative is used to set the problem.
Idris Ahmed, Poom Kumam, K. Shah, Piyachat Borisut, K. Sitthithakerngkiet, Musa A. Demba   +5 more
semanticscholar   +1 more source

Weyl Quantization of Fractional Derivatives

, 2009
The quantum analogs of the derivatives with respect to coordinates q_k and momenta p_k are commutators with operators P_k and $Q_k. We consider quantum analogs of fractional Riemann-Liouville and Liouville derivatives.
Kilbas A. A., Miller K., Oldham K. B., Podlubny I., Samko S. G., Tarasov V. E., Vasily E. Tarasov, Yosida K., Zaslavsky G. M.   +8 more
core   +1 more source

Gauge invariance in fractional field theories [PDF]

, 2008
The principle of local gauge invariance is applied to fractional wave equations and the interaction term is determined up to order $o(\bar{g})$ in the coupling constant $\bar{g}$.
Abers, Baleanu, Baleanu, Caputo, Chiu, Edmonds, Feller, Goldfain, Grünwald, Herrmann, Herrmann, Lim, Liouville, Miller, Oldham, Pauli, Podlubny, Raspini, Raspini, Richard Herrmann, Riemann, Riesz, Sakurai, Weyl, Wilson, Yang, Yao, Zavada, Zeeman   +28 more
core   +1 more source

Fast algorithms for convolution quadrature of Riemann-Liouville fractional derivative [PDF]

Applied Numerical Mathematics, 2019
32 pages, 2 ...
Daxin Nie, Jing Sun, Weihua Deng
openaire   +2 more sources

Existence of Solutions for Riemann-Liouville Fractional Boundary Value Problem

Abstract and Applied Analysis, 2014
By using the method of upper and lower solutions and fixed point theorems, the existence of solutions for a Riemann-Liouville fractional boundary value problem with the nonlinear term depending on fractional derivative of lower order is obtained under ...
Wenzhe Xie, Jing Xiao, Zhiguo Luo
doaj   +1 more source

Lie symmetry analysis, conservation laws and exact solutions of the seventh-order time fractional Sawada–Kotera–Ito equation

Results in Physics, 2016
In this paper Lie symmetry analysis of the seventh-order time fractional Sawada–Kotera–Ito (FSKI) equation with Riemann–Liouville derivative is performed.
Emrullah Yaşar, Yakup Yıldırım, Chaudry Masood Khalique   +2 more
doaj   +1 more source

The Approximate Analytic Solution of the Time-Fractional Black-Scholes Equation with a European Option Based on the Katugampola Fractional Derivative

Mathematics, 2021
In the finance market, it is well known that the price change of the underlying fractal transmission system can be modeled with the Black-Scholes equation.
Sivaporn Ampun, Panumart Sawangtong
doaj   +1 more source

Fractional Newton-Raphson Method Accelerated with Aitken's Method

, 2019
The Newton-Raphson (N-R) method is characterized by the fact that generating a divergent sequence can lead to the creation of a fractal, on the other hand the order of the fractional derivatives seems to be closely related to the fractal dimension, based
Brambila-Paz, F., Caballero-Cruz, R., Iturrarán-Viveros, U., Torres-Hernandez, A.   +3 more
core   +1 more source

Optimal error estimate of the Legendre spectral approximation for space-fractional reaction–advection–diffusion equation

Advances in Difference Equations, 2018
In this paper, we consider the space-fractional reaction–advection–diffusion equation with fractional diffusion and integer advection terms. By treating the first-order integer derivative as the composition of two Riemann–Liouville fractional derivative ...
Wenping Chen, Shujuan Lü, Hu Chen, Haiyu Liu   +3 more
doaj   +1 more source