We consider a Cauchy problem for the inhomogeneous differential equation given in terms of an unbounded linear operator A and Caputo fractional derivative order α∈(0,2) time. The previously known representation mild solution to such does not have conventional variation-of-constants like form, with propagator derived from associated homogeneous problem. Instead, it relies on existence two propag...

Abstract The evolution by horizontal mean curvature flow (HMCF) is a partial differential equation in sub-Riemannian setting with applications IT and neurogeometry [see Citti et al. (SIAM J Imag Sci 9(1):212–237, 2016)]. Unfortunately this difficult to study, since the normal not always well defined. To overcome problem Riemannian approximation was introduced. In article we obtain stochastic re...

Let U(t, ) be solution of the Dirichlet problem y''+( t-q(t))y= 0 - 1 t l y(-l)= 0 = y(x), with variabIe t on (-1, x), for fixed x, which satisfies the initial condition U(-1, )=0 , (-1, )=1. In this paper, the asymptotic representation of the corresponding eigenfunctions of the eigen values has been investigated . Furthermore, the leading term of the asymptotic formula for ...

This research describes the unsteady two-dimensional reacting flows around a circular cylinder. The numerical solution combines the random vortex method for incompressible two-dimensional viscous fluid flow with a Simple Line Interface Calculation (SLIC) algorithm for the propagation of flame interface. To simplify the governing equations, two fundamental assumptions namely Low Mach Number and ...