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 1: of Epidemiology, impact and control of bovine cysticercosis in Europe: a systematic review

PRISMA 2009 Checklist. (DOC 65 kb

Additional file 3: of Epidemiology, impact and control of bovine cysticercosis in Europe: a systematic review

Prevalence data extracted from the included records. (DOCX 98 kb

Additional file 2: of Epidemiology, impact and control of bovine cysticercosis in Europe: a systematic review

List of references for the records included in the review. (XLSX 20 kb

Sero-epidemiological studies using Ag-ELISA and/or EITB for human cysticercosis in Africa.

<p>Legend: YOP: Year of publication; Location: Corresponds to the Province, State, Region or Department in which the communities where the studies took place are located; Ag: Antigen detection based on Ag-ELISA results; Ab: Antibody detection based on EITB results; 95% CI: 95% Confidence Intervals; REMEP: Random Effects Model Estimated Prevalence; Dem. Rep. of Congo: Democratic Republic of Congo.</p><p>^a: Results obtained from B158/B60 Ag-ELISA</p><p>^b: Results obtained from HP10 Ag-ELISA.</p><p>Sero-epidemiological studies using Ag-ELISA and/or EITB for human cysticercosis in Africa.</p

Flow diagram describing literature search and selection of studies (PRISMA 2009 flow chart).

<p>Flow diagram describing literature search and selection of studies (PRISMA 2009 flow chart).</p

Sero-epidemiological studies using Ag-ELISA and/or EITB for human cysticercosis in Asia.

<p>Legend: YOP: Year of publication; Location: Corresponds to the Province, State, Region or Department in which the communities are located where the studies took place; Ag: Antigen detection based on Ag-ELISA results; Ab: Antibody detection based on EITB results; 95% CI: 95% Confidence Intervals; REMEP: Random Effects Model Estimated Prevalence</p><p>^a: Results obtained from B158/B60 Ag-ELISA</p><p>Sero-epidemiological studies using Ag-ELISA and/or EITB for human cysticercosis in Asia.</p

Global distribution of the endemic countries where Ag-ELISA and/or EITB based epidemiological studies were held.

<p>Light yellow represents the countries confirmed as endemic by the World Health Organization (WHO) until 2012 [<a href="http://www.plosntds.org/article/info:doi/10.1371/journal.pntd.0003919#pntd.0003919.ref066" target="_blank">66</a>]. Circles represent the countries where Ag-ELISA based studies took place. Each color represents the average prevalence per country found from the selected articles in this review classified in 0 to 5 percent; 5 to 10 percent and more than 10 percent. Triangles represent the countries where EITB based studies took place. Each color represents the average prevalence per country found from the selected articles in this review classified in 0 to 5 percent; 5 to 10 percent and more than 10 percent.</p

Factors affecting serological variations of human cysticercosis infection and exposure to <i>T</i>. <i>solium</i> eggs.

<p>Factors affecting serological variations of human cysticercosis infection and exposure to <i>T</i>. <i>solium</i> eggs.</p

Sero-epidemiological studies using Ag-ELISA and/or EITB for human cysticercosis in Latin America.

<p>Legend: YOP: Year of publication; Location: Corresponds to the Province, State, Region or Department in which the communities are located where the studies took place; Ag: Antigen detection based on Ag-ELISA results; Ab: Antibody detection based on EITB results; 95% CI: 95% Confidence Intervals; REMEP: Random Effects Model Estimated Prevalence</p><p>^a: Results obtained from B158/B60 Ag-ELISA</p><p>^b: Results obtained from HP10 Ag-ELISA</p><p>N.A.: Not available.</p><p>Sero-epidemiological studies using Ag-ELISA and/or EITB for human cysticercosis in Latin America.</p