Résumé:
The main objective of this thesis is to present an analytical and numerical contribution of
certain fractional boundary problems according to different approaches. Original results ensuring the existence
and uniqueness/existence as well as stability of solutions are discussed for some new problems
involving fractional order operators. In addition, an approach for solving a type of fractional linear problems
with boundary conditions is developed and some applications are presented, where the validity and
accuracy of this scheme are shown.
The analytical results of this thesis focus on the application of some fixed point theorems and certain
types of Ulam stability to address two proposed fractional problems. The first problem concerns the Van de
Pol Duffing (VDPD)-Jerk oscillator, while the second one involves the pantograph type equation, utilizing
the Caputo-Hadamard approach. Illustrative examples will be provided to demonstrate the validity of the
results.
We devote a final part of our project to numerical results, where an approach is developed to approximate
the solutions of a class of fractional linear boundary value problems and some applications are presented
in this context.
