We then calculate the wave function of the time fractional Schrdinger using the inverse Laplace transform together considering the Schouten-Vanderpol theorem and some special circumstances of the problem. The o
print "ERROR: Inverse transform can not be calculated for t=0" return ("Error"); # The for loop is evaluating the Laplace inversion at each point theta which is based on the trapezoidal rule for k in range(0,N): theta = -pi + (k+1./2)*h; z = shift + N/t*(0.5017*theta*c...
All plots in this work have been generated bymatplotlib[84], which is an open-source Python 2D plotting library, producing publication-quality figures in a variety of hardcopy formats and interactive environments across platforms. Instead, illustration sketches have been created by LatexDraw [9], a...
In order to infer the last inequality, we use Hölder's inequality and inverse estimates. In order to pass from the mass-lumped inner product to the standard L2( ) inner product, other occurring terms have to be estimated in the same fashion, but locally. Regarding the second term, we ...
being 𝐹(𝑠)=𝑠−𝛼 the Laplace transform of the kernel 𝑡𝛼−1/Γ(𝛼) in (1). The assumptions that make possible this generalization of LMMs are that the generating function 𝛿(𝜉) has no zeros in the closed unit disc |𝜉|≤1, except for 𝜉=1, and |arg𝛿(...