in the present paper, measure differential equations involving the distributional henstock-kurzweil integral are investigated. theorems on the existence and structure of the set of solutions are established by using schauder$^prime s$ fixed point theorem and vidossich theorem. two examples of the main results paper are presented. the new results are generalizations of some previous results in t...

In this paper we prove the SBV regularity of the distributional derivative of a viscosity solution of the Hamilton-Jacobi equation ∂tu + H(t, x, Dxu) = 0 in Ω ⊂ [0, T ]× R, under the hypothesis of uniform convexity of the Hamiltonian H in the last variable. This result extends the result of Bianchini, De Lellis and Robyr obtained for an Hamiltonian H = H(Dxu) which depends only on the spatial d...

This paper establishes some closed formulas for RiemannLiouville impulsive fractional integral calculus and also for RiemannLiouville and Caputo impulsive fractional derivatives. Keywords—RimannLiouville fractional calculus, Caputo fractional derivative, Dirac delta, Distributional derivatives, Highorder distributional derivatives.

Let \(\Omega\subset\mathbf{R}^3\) be a domain and let \(f\colon\Omega\to\mathbf{R}^3\) bi-\(BV\) homeomorphism. Very recently in [16] it was shown that the distributional adjugate of \(Df\) (and thus also \(Df^{-1}\)) is matrix-valued measure. In present paper we show components Adj coincide with \(Df^{-1}(f(U))\) as measures absolutely continuous part equals to pointwise adj \(Df(x)\) a.e. We ...

We extend the construction of the authors’ paper of 2002 by introducing spaces of generalized tensor fields on smooth manifolds that possess optimal embedding and consistency properties with spaces of tensor distributions in the sense of L. Schwartz. We thereby obtain a universal algebra of generalized tensor fields canonically containing the space of distributional tensor fields. The canonical...

In this paper, we investigate the existence of nontrivial solutions in Bessel Potential space for nonlinearfractional Schrödinger-Poisson system involving distributional Riesz fractional derivative. By using themountain pass theorem combination with perturbation method, prove solutions.

Two approaches for defining fractional derivatives of periodic distributions are presented. The first is a distributional version of the Weyl fractional derivative in which a derivative of arbitrary order of a periodic distribution is defined via Fourier series. The second is based on the Grünwald-Letnikov formula for defining a fractional derivative as a limit of a fractional difference quotie...

The semantic behavior of derivational processes has been investigated with compositional distributional models relating the meaning of base, affix, and derivative (e.g., anti+capitalist→ anticapitalist). While broadly successful, these approaches model how the distributional behavior generally is affected by derivation. Meanwhile, their predictions can not be interpreted at the level of linguis...