Applications Des Inégalités Intégrales Aux Problèmes Aux Limites D Ordre Arbitraire

Résumé: 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.

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