Abstract:
In this thesis we give a brief history and definition of fractional
calculus and we discuss standard approaches to problems of fractional
derivatives and fractional integrals namely the Riemann-Liouville, the
Caputo respectively. Then we introduce some basic definitions and facts
on partial fractional calculus theory and fixed-points theory, we give
some generalizations of Gronwall’s lemmas for two independent
variables. Also we concern by existence of solutions to fractional order
partial functional differential equations. Finally we apply the modified
variational iteration method to give analytical solutions of fractional
differential equations.
