In this work we consider the abstract Cauchy problem with Caputo fractional time derivative of order $$\alpha \in (0,1]$$ , and discuss continuity respective solutions regarding parameter $$ . We also present a study about Mittag-Leffler families operators (for ), when they are induced by sectorial operators.

The analysis of 90 • vortex-vortex scattering is extended to π n scattering in all head-on collisions of n vortices in the Abelian Higgs model. A Cauchy problem with initial data that describe the scattering of n vortices is formulated. It is shown that this Cauchy problem has a unique global finite-energy solution. The symmetry of the solution and the form of the local analytic solution then s...

We present an exponentially convergent numerical method to approximate the solution of Cauchy problem for inhomogeneous fractional differential equation with unbounded operator coefficient and Caputo derivative in time. The is based on newly obtained formula that consolidates mild representations sub-parabolic, parabolic sub-hyperbolic equations sectorial $A$ non-zero initial data. involved int...

We study the stability in the Cauchy Problem for the Helmholtz equation in dependence of the wave number k. For simple geometries, we show analytically that this problem is getting more stable with increasing k. In more detail, there is a subspace of the data space on which the Cauchy Problem is well posed, and this subspace grows with larger k. We call this a subspace of stability. For more ge...

Abstract A mathematical model is developed to determine the steady-state electric current flow through in non-homogeneous isotropic conductor whose shape has a three-dimensional hollow body. The equations of Maxwell's theory solid body are used formulate corresponding boundary value problem. determination steady motion charges based on concept electrical conductance. derivation upper and lower ...