3 research outputs found
A novel approach to fractional calculus: utilizing fractional integrals and derivatives of the Dirac delta function
While the definition of a fractional integral may be codified by Riemann and
Liouville, an agreed-upon fractional derivative has eluded discovery for many
years. This is likely a result of integral definitions including numerous
constants of integration in their results. An elimination of constants of
integration opens the door to an operator that reconciles all known fractional
derivatives and shows surprising results in areas unobserved before, including
the appearance of the Riemann Zeta Function and fractional Laplace and Fourier
Transforms. A new class of functions, known as Zero Functions and closely
related to the Dirac Delta Function, are necessary for one to perform
elementary operations of functions without using constants. The operator also
allows for a generalization of the Volterra integral equation, and provides a
method of solving for Riemann's "complimentary" function introduced during his
research on fractional derivatives
Additional file 2: Table S1. of Abundance, zoonotic potential and risk factors of intestinal parasitism amongst dog and cat populations: The scenario of Crete, Greece
Binary logistic model for Giardia spp. infection rate in dogs. Table S2. Zero-inflation negative binomial model for parasite infection intensity in dog samples. (DOCX 17Â kb
Additional file 1: Table S1. of Epidemiology of taeniosis/cysticercosis in Europe, a systematic review: Western Europe
PRISMA 2009 Checklist. (DOC 64 kb