Título: **
Fractional Calculus: basic theory and applications (Part I).
**

Autores: **
Diego del-Castillo-Negrete
**

**Resumen**

Here we introduce the notion of fractional integral as a straightforward
generalization of the standard, integer-order integral, and define the
fractional derivative as the inverse operation. To motivate the concept we
discuss two examples: Abel's equation and heat diffusion. The concepts
discussed here are further elaborated in the next section.

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