We study the relation between standard ideals of the convolution Sobolev algebra ${₊}^{\left(n\right)}\left(tⁿ\right)$ and the convolution Beurling algebra L¹((1+t)ⁿ) on the half-line (0,∞). In particular it is proved that all closed ideals in ${₊}^{\left(n\right)}\left(tⁿ\right)$ with compact and countable hull are standard.

We are concerned with first order set-valued problems with very general boundary value conditions $$\left\{\begin{array}{c}{u}_g^{\text{'}}\left(t\right)\in F(t,u\left(t\right)),{\mu }_g\text{-a.e.}\in [0,T],\hfill \\ L\left(u\right(0),T))=0\hfill \end{array}\right.$$ involving the Stieltjes derivative with respect to a left-continuous nondecreasing function $g:[0,T]\to ℝ$, a Carathéodory multifunction $F:[0,T]\times ℝ\to 𝒫\left(ℝ\right)$ and a continuous $L:{ℝ}^2\to ℝ$. Using appropriate notions of lower and upper solutions, we prove the existence of solutions via a fixed point result for condensing mappings. In the periodic single-valued case, combining an existence theory for the linear case with a recent result involving...

We study a stochastic fractional partial differential equations of order $\alpha \>1$ driven by a compensated Poisson measure. We prove existence and uniqueness of the solution and we study the regularity of its trajectories.

Mathematics Subject Classification: 26A33, 76M35, 82B31A stochastic solution is constructed for a fractional generalization of the KPP (Kolmogorov, Petrovskii, Piskunov) equation. The solution uses a fractional generalization of the branching exponential process and propagation processes which are spectral integrals of Levy processes.

MSC 2010: 26A33, 34A08, 34K37

In this article, we present a new method for converting the boundary value problems for impulsive fractional differential systems involved with the Riemann-Liouville type derivatives to integral systems, some existence results for solutions of a class of boundary value problems for nonlinear impulsive fractional differential systems at resonance case and non-resonance case are established respectively. Our analysis relies on the well known Schauder’s fixed point theorem and coincidence degree theory....

Let ϕ be an arbitrary bijection of ${ℝ}_{+}$. We prove that if the two-place function ${\varphi }^{-1}[\varphi \left(s\right)+\varphi \left(t\right)]$ is subadditive in ${ℝ}_{+}^2$ then $\varphi$ must be a convex homeomorphism of ${ℝ}_{+}$. This is a partial converse of Mulholland’s inequality. Some new properties of subadditive bijections of ${ℝ}_{+}$ are also given. We apply the above results to obtain several converses of Minkowski’s inequality.

Results on integration by parts and integration by substitution for the variational integral of Henstock are well-known. When real-valued functions are considered, such results also hold for the Generalized Riemann Integral defined by Kurzweil since, in this case, the integrals of Kurzweil and Henstock coincide. However, in a Banach-space valued context, the Kurzweil integral properly contains that of Henstock. In the present paper, we consider abstract vector integrals of Kurzweil and prove Substitution...

We consider the dynamical system (𝒜, Tf), where 𝒜 is a class of differential real functions defined on some interval and Tf : 𝒜 → 𝒜 is an operator Tfφ := fοφ, where f is a differentiable m-modal map. If we consider functions in 𝒜 whose critical values are periodic points for f then, we show how to define and characterize a substitution system associated with (𝒜, Tf). For these substitution systems, we compute the growth rate of the...

Mathematics Subject Classification: 26A33 (main), 35A22, 78A25, 93A30The generalization of the concept of derivative to non-integer values goes back to the beginning of the theory of differential calculus. Nevertheless, its application in physics and engineering remained unexplored up to the last two decades. Recent research motivated the establishment of strategies taking advantage of the Fractional Calculus (FC) in the modeling and control of many phenomena. In fact, many classical engineering...

We present a new method to study the classical fractional integrals of Weyl. This new approach basically consists in considering these operators in the largest space where they make sense. In particular, we construct a theory of fractional integrals of Weyl by studying these operators in an appropriate Fréchet space. This is a function space which contains the $L^p\left(ℝ\right)$-spaces, and it appears in a natural way if we wish to identify these fractional operators with fractional powers of a suitable non-negative...