At present, the use of fractional order partial differential equation in real-physical systems is commonly encountered in the fields of science and engineering.
The efficient computational tools are required for analytical and numerical approximations of such physical models..
Fractional calculus is a collection of relatively little-known mathematical results concerning generalizations of differentiation and integration to noninteger orders..
Fractional calculus is deeply related to the dynamics of complicated real-world problems.
Fractional operators are non-local and describe several natural phenomena in a better and systematic manner.
Many mathematical models are accurately governed by fractional order differential equations..
Fractional calculus is used in computer vision for enhancement, better detection selectivity, developing robust denoising models, and dealing with discontinuities.
Unlike integer-order derivatives, the non-local nature of fractional derivatives helps in gathering past and surrounding information..
The application of the fractional calculus can be very useful for the modeling of anomalous diffusion phenomena in which the fractal structure better reflects the real conditions of the medium, as it is the case of the reservoirs in which because of its very nature it is difficult to find a structure Euclidian..
Fractional Calculus (FC) was a bright idea of Gottfried Leibniz originating in the end of the seventeenth century.
The topic was developed mainly in a mathematical framework, but during the last decades FC was recognized to represent an useful tool for understanding and modeling many natural and artificial phenomena..
This means that N.
H.
Abel, who was only 21 years of age at the time of the publication of his paper, was the father of the complete fractional-order calculus framework..
