the complex-step derivative approximation is applied to compute numerical derivatives. in this study, we propose a new formula of fractional complex-step method utilizing jumarie definition. based on this method, we illustrated an approximate analytic solution for the fractional cauchy-euler equations. application in image denoising is imposed by introducing a new fractional mask depending on s...

In this note we examine the solution and the impulsive behavior of autonomous linear multivariable systems whose pseudo-state β (t) obeys a linear matrix differential equation A (ρ)β (t) = 0 where A (ρ) is a polynomial matrix in the differential operator ρ := d dt . We thus generalize to the general polynomial matrix case some results obtained in [2][3] which regard the impulsive behavior of th...

We consider the perturbation of parabolic operators of the form ∂t + P (x,D) by large-amplitude highly oscillatory spatially dependent potentials modeled as Gaussian random fields. The amplitude of the potential is chosen so that the solution to the random equation is affected by the randomness at the leading order. We show that, when the dimension is smaller than the order of the elliptic pseu...

We study the asymptotics of fundamental solutions of p-adic pseudodifferential equations of type (f(∂, β) + λ)u = g, where f(∂, β) is a pseudo-differential operator with symbol |f | K , β > 0, f is a form of arbitrary degree with coefficients in a p−adic field, λ ≥ 0, and g is a Schwartz-Bruhat function.

We investigate connections between certain dispersive estimates of a (pseudo)differential operator of real principal type and the number of nonvanishing curvatures of its characteristic manifold. More precisely, we obtain sharp thresholds for the range of Lebesgue exponents depending on the specific geometry.

We establish a parameter-dependent pseudo-differential calculus on an infinite cylinder, regarded as a manifold with conical exits to infinity. The parameters are involved in edge-degenerate form, and we formulate the operators in terms of operator-valued amplitude functions. Mathematics Subject Classification (2000). Primary 35S35; Secondary 35J70.

In this paper, we consider a certain class of discrete pseudo-differential operators in a sharp convex cone and describe their invertibility conditions in L2-spaces. For this purpose we introduce a concept of periodic wave factorization for elliptic symbol and show its applicability for the studying. Key–Words: Discrete operator, Multidimensional periodic Riemann problem, Periodic wave factoriz...

Fourier integral operators, for the calculus of which I refer to Hörmander [17], have been applied in essentially two ways: as similarity transformations and in the description of the solutions of genuinely nonelliptic (pseudo-) differential equations. The first application is based on the observation of Egorov [12] that if P9 resp. g, is a pseudo-differential operator with principal symbol equ...