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With the discovery of new superconductors there was a running to find thejustifications for the new properties found in these materials. In order todescribe these new effects some theories were adapted and some others have beentried. In this work we present an application of the fractional calculus tostudy the superconductor in the context of London theory. Here we investigatedthe linear London equation modified by fractional derivatives fornon-differentiable functions, instead of integer ones, in a coarse grainedscenario. We apply the fractional approach based in the modifiedRiemann-Liouville sense to improve the model in order to include possiblenon-local interactions and the media. It is argued that the e ects ofnon-locality and long memory, intrinsic to the formalism of the fractionalcalculus, are relevant to achieving a satisfactory phenomenologicaldescription. In order to compare the present results with the usual Londontheory, we calculated the magnetic field distribution for a mesoscopicsuperconductor system. Also, a fractional Pippard-like model is proposed totake into account the non-locality beside effects of interactions and themedia. We propose that parameter alfa of fractionality can be used to create analternative way to characterize superconductors.

The Fractional London Equation and The Fractional Pippard Model For Superconductors