In this article we study a new class of boundary value problems for fractional differential equations and inclusions with multiple orders of fractional derivatives and integrals, in both fractional differential equation and boundary conditions. The Sadovski’s fixed point theorem is applied in the single-valued case while, in multi-valued case, the nonlinear alternative for contractive maps is u...

It turns out that various algebraic computations can be reduced to the same type of computations: one has to study the series of integrals ∫ K f(k)g(k) dk, where f, g are complex valued K-finite functions on a compact Lie group K. So it is tempting to state a general conjecture about the behavior of such integrals, and to investigate the consequences of the conjecture. Main conjecture: Let K be...

We develop a theory of Malliavin calculus for Banach space valued random variables. Using radonifying operators instead of symmetric tensor products we extend the Wiener-Itô isometry to Banach spaces. In the white noise case we obtain two sided L-estimates for multiple stochastic integrals in arbitrary Banach spaces. It is shown that the Malliavin derivative is bounded on vector-valued Wiener-I...

In this paper, we define a new and broad family of vector-valued random fields called tempered operator fractional operator-stable (TRF, for short). TRF is typically non-Gaussian generalizes stable stochastic processes. comprises moving average harmonizable-type subclasses that are constructed by tempering (matrix-) homogeneous, matrix-valued kernels in time- Fourier-domain integrals with respe...

The aim of this paper is to establish the vector-valued inequalities for Littlewood-Paley operators, including the Lusin area integrals, the Littlewood-Paley g-functions and g∗μ-functions, and their commutators on the Herz-Morrey spaces with variable exponentMK̇ p,q(·)(R n). By applying the properties of Lp(·)(Rn) spaces and the vector-valued inequalities for Littlewood-Paley operators and their...

The main results of this paper are a Cell Decomposition Theorem for Henselian valued fields with analytic structure in an analytic Denef-Pas language, and its application to analytic motivic integrals and analytic integrals over Fq((t)) of big enough characteristic. To accomplish this, we introduce a general framework for Henselian valued fields K with analytic structure, and we investigate the...

In [3] we introduced a “monotone-type” (that is, Choquet-type) integral for realvalued functions, with respect to finitely additive positive set functions, with values in a Dedekind complete Riesz space. A “Lebesgue-type” integral for such kind of functions was investigated in [7]. In [4] we gave some comparison results for these types of integrals. In [10], a Choquet-type integral for real-val...

Summary The goal of this article is to clarify the relationship between Riemann and Lebesgue integrals. In previous [5], we constructed a one-dimensional measure. measure provides any intervals, which can be used prove well-known [6] integrals [1]. We also proved integral given that its complete As result work, bounded real valued function in Mizar system [2], [3] calculated by integral.