SUR LE (p,q)-CALCUL FRACTIONNAIRE

Abstract

Le but principal de ce mÈmoire consiste en líÈtude de concepts et rÈsultats les plus importants de la thÈorie du (p; q)-calcul fractionnaire en Ètudiant notament la (p; q)-dÈrivÈe fractionnaire et la (p; q)-intÈgrale fractionnaire ainsi que leurs propriÈtÈs ÈlÈmentaires. on donne Ègalement une application aux Èquations aux q-dÈrivÈes partielles ainsi quíune application de la (p; q)-transformation de Laplace ‡ certaines Èquations aux (p; q)-di§Èrentelles.

The main purpose of this thesis consists in the study of the most important concepts and results of the theory of (p; q)-fractional calculus by studying in particular the (p; q)- fractional derivative and the (p; q)-fractional integral and their basic properties. we also give an application to partial q-derivative equations as well as an application of the (p; q)-Laplace transformation to certain (p; q)-di§erential equations.