Publication: Contributions to conformable and non-conformable calculus
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2019-09
Defense date
2019-12-03
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Abstract
In this work, we introduce a definition of a local fractional derivative and a fractional
integral of order alfa > 0 (where this parameter does not need to be integer), with
which we overcome some deficiencies of known local derivatives, conformable or not.
This definition allows to compute fractional derivatives of functions defined on any
open set on the real line (and not just on the positive half-line). Moreover, we extend
some classical results to the context of fractional derivatives. Also, applications of
the fractional derivative through the direct and inverse problems are shown, as well
as the feasibility of the fractional calculus in real and simulated problems.
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Keywords
Fractional calculus, Fractional differential equations, Fractional conformable derivatives, Fracitional integrals, Drude model, Lienard-type systems, Numerical solutions