This thesis is concerned basically with establishing theoretical background for the Riemann-Liouville definition of fractional differentiation and integration of the function of several variables and solving certain type of fractional partial differential equations using some approximated methods.
The first objectives of this thesis, is oriented towards function approximation using special type of spline, which is called the "G-spline" including the details of the subject and the proof of some lemmas and corollary for completeness. The second objective of this work is the generalization of G-spline functions for two-dimensional spaces including the statement and proof of the existence and uniqueness theorems as well as the statement and proof of the optimality of two-dimensional G-spline functions.
Planar noninvertible maps have been studied recently by several authors such as Mira , Gardini , Cathala.
