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pro vyhledávání: '"34a08"'
This paper discusses some unusual consequences raised by the definition of the conformable derivative in the lower terminal. A replacement for this definition is proposed and statements adjusted to the new definition are presented.
Externí odkaz:
http://arxiv.org/abs/2409.02944
Autor:
Choi, Brian
We study the formation of breathers in multi-dimensional lattices with nonlocal coupling that decays algebraically. By variational methods, the exact relationship between various parameters (dimension, nonlinearity, nonlocal parameter $\alpha$) that
Externí odkaz:
http://arxiv.org/abs/2408.11177
This paper introduces nonlinear fractional Lane-Emden equations of the form, $$ D^{\alpha} y(x) + \frac{\lambda}{x^\beta}~ D^{\beta} y(x) + f(y) =0, ~ ~1 < \alpha \leq 2, ~~ 0< \beta \leq 1, ~~ 0 < x < 1,$$ subject to boundary conditions, $$ y'(0) =\
Externí odkaz:
http://arxiv.org/abs/2408.10212
In this paper we report a few numerical tests by using a slight extension of the Matlab code fhbvm in [8], implementing Fractional HBVMs, a recently introduced class of numerical methods for solving Initial Value Problems of Fractional Differential E
Externí odkaz:
http://arxiv.org/abs/2407.11460
Autor:
Zitane, Hanaa, Torres, Delfim F. M.
This work deals with the finite time stability of generalized proportional fractional systems with time delay. First, based on the generalized proportional Gr\"onwall inequality, we derive an explicit criterion that enables the system trajectories to
Externí odkaz:
http://arxiv.org/abs/2405.12256
Autor:
Yin, Daopeng, Mei, Liquan
In this work, we will give proper estimates for the discrete convolution complementary (DCC) kernels, which leads to the asymptotically compatible fractional Gr\"onwall inequality. The consequence can be applied in the analysis of the stability and p
Externí odkaz:
http://arxiv.org/abs/2404.19170
Autor:
Torres, Delfim F. M.
Publikováno v:
Mediterr. J. Math. 21 (2024), no. 3, Paper No. 106, 16pp
Through duality it is possible to transform left fractional operators into right fractional operators and vice versa. In contrast to existing literature, we establish integration by parts formulas that exclusively involve either left or right operato
Externí odkaz:
http://arxiv.org/abs/2404.14458
In the present study, we consider the numerical method for Toeplitz-like linear systems arising from the $d$-dimensional Riesz space fractional diffusion equations (RSFDEs). We apply the Crank-Nicolson (CN) technique to discretize the temporal deriva
Externí odkaz:
http://arxiv.org/abs/2404.10221
Autor:
Jornet, Marc
We show how a rescaling of fractional operators with bounded kernels may help circumvent their documented deficiencies, for example, the inconsistency at zero or the lack of inverse integral operator. On the other hand, we build a novel class of line
Externí odkaz:
http://arxiv.org/abs/2403.06198
Publikováno v:
Numerical Algorithms (2024)
In this paper we describe the efficient numerical implementation of Fractional HBVMs, a class of methods recently introduced for solving systems of fractional differential equations. The reported arguments are implemented in the Matlab code fhbvm, wh
Externí odkaz:
http://arxiv.org/abs/2403.04916