We consider a basic fractional differential inequality with a fractional derivative named after Hilfer and a polynomial source. A non-existence of global solutions result is proved in an appropriate space and the critical exponent is shown to be optimal.

Pearson diffusions are governed by diffusion equations with polynomial coefficients. Fractional Pearson diffusions are governed by the corresponding time-fractional diffusion equation. They are useful for modeling sub-diffusive phenomena, caused by particle sticking and trapping. This paper provides explicit strong solutions for fractional Pearson diffusions, using spectral methods. It also pre...

We study the complexity of computing equilibria in two classes of network games based on flows fractional BGP (Border Gateway Protocol) games and fractional BBC (Bounded Budget Connection) games. BGP is the glue that holds the Internet together and hence its stability, i.e. the equilibria of fractional BGP games [15], is a matter of practical importance. BBC games [21] follow in the tradition o...

Objective: This study uses a flexible nonlinear approach, Fractional polynomial models (FPs), to examine the association between obesity and C-reactive protein to select the best fitted model within 44 potentially FP models. Methods: Data for 5 years (2001-2010) of the National Health Interview Survey (NHANES) was used. All respondents aged between 17 and 74 were included in the analysis. CRP w...

Mendelian randomization, the use of genetic variants as instrumental variables (IV), can test for and estimate the causal effect of an exposure on an outcome. Most IV methods assume that the function relating the exposure to the expected value of the outcome (the exposure-outcome relationship) is linear. However, in practice, this assumption may not hold. Indeed, often the primary question of i...

The truncated Fourier series exhibits oscillation that does not disappear as the number of terms in the truncation is increased. This paper introduces 2-D fractional Fourier series (FrFS) according to the 1-D fractional Fourier series, and finds such a Gibbs oscillation also occurs in the partial sums of FrFS for bivariate functions at a jump discontinuity. In this study, the 2-D inverse polyno...

This paper is devoted to the study of the flatness property of linear time-invariant differential systems of fractional systems. We give two characterizations of fractionally flat outputs and algorithms to compute them. We then present an application to a two dimensional thermal system that we approximate by a fractional model of order 1 2 , that is fractionally flat. Trajectory planning of the...

Abstract Let $E\subset{\mathbb{R}}$ be a closed set of Hausdorff dimension $\alpha \in (0, 1)$. $P: {\mathbb{R}}\to{\mathbb{R}}$ polynomial without constant term whose degree is bigger than one. We prove that if $E$ supports probability measure satisfying certain condition and Fourier decay condition, then contains three points $x, x+t, x+P(t)$ for some $t>0$. Our result extends the one ...