Applications des Inégalités Intégrales aux Problèmes aux Limites d Ordre Arbitraire

Abstract

The work of this thesis focuses on the application of integral inequalities to boundary value problems of arbitrary order. Integral inequalities play an important role in the theory of di¤erential equations and applied sciences. Moreover, the fractional type inequalities are also quite important that the applications are numerous, including fractional theory of di¤erential equations, theoretical approximations in probability and statistics. In this thesis, we present some results of fractional order on estimates of (r; )􀀀fractional moments using the Riemann-Liouville fractional integral theory. Also by applying the k􀀀fractional Riemann-Liouville integral we give some results on estimates of k􀀀fractional dispersion and k􀀀fractional variance. Next, we are interested at the applications of fractional integral in- equalities to study a boundary value problem of arbitrary order in a Banach space. Finally, we treat the question of existence and uniqueness of the solution of a system of fractional di¤erential equations.