Journal
CALCOLO
Volume 54, Issue 3, Pages 903-917Publisher
SPRINGER-VERLAG ITALIA SRL
DOI: 10.1007/s10092-017-0213-8
Keywords
General conformable fractional derivative; Conformable fractional derivative; Fractional conformable function; Extended Gateaux derivative; Linear Extended Gateaux derivative; Physical interpretation; Geometrical interpretation; Local fractional derivative
Categories
Funding
- National Natural Science Foundation of China [11171238]
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Fractional calculus is a powerful and effective tool for modelling nonlinear systems. In this paper, we introduce a class of new fractional derivative named general conformable fractional derivative (GCFD) to describe the physical world. The GCFD is generalized from the concept of conformable fractional derivative (CFD) proposed by Khalil. We point out that the term in CFD definition is not essential and it is only a kind of fractional conformable function. We also give physical and geometrical interpretations of GCFD which thus indicate potential applications in physics and engineering. It is easy to demonstrate that CFD is a special case of GCFD, then to the authors' knowledge, so far we first give the physical and geometrical interpretations of CFD. The above work is done by a new framework named Extended GA cent teaux derivative and Linear Extended GA cent teaux derivative which are natural extensions of GA cent teaux derivative. As an application, we discuss a scheme for solving fractional differential equations of GCFD.
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