Browsing by Author "Djiab, Somia"
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Item Open Access Contributions aux équations aux dérivées fractionnaires conformables(Université de M'sila, 2022-05) Djiab, Somian this thesis, we have studied four problems of three types of fractional differential equations with integral boundary conditions: ✓ At first, their solutions are presented in form of nonlinear integral equations by using the Green function, which her properties are analyzed to determine the appropriate way to solve the proposed problems. ✓ Secondly, we proved the positivity, existence and uniqueness of solutions to the proposed problems by using some fixed theorems. ✓ Next, we give a new results concerning the stability of fractional equations in Ulam-Hyres sense to prove the stability of solutions for proposed problems. ✓ Finally, several examples are presented to confirm the effectiveness of some utilized theorems.Item Open Access This paper deals with a boundary value problem for a nonlin- ear di erential equation with two conformable fractional derivatives and integral boundary conditions. The results of existence, uniqueness and stability of positive solutions are proved by using the Banach contrac- tion principle, Guo-Krasnoselskii's xed point theorem and Hyers-Ulam type stability. Two concrete examples are given to illustrate the main results. Mathematics Subject Classi cation (2010): 47H10, 26A33, 34B18.(Université de M'sila, 2021) Djiab, SomiaThis paper deals with a boundary value problem for a nonlin- ear di erential equation with two conformable fractional derivatives and integral boundary conditions. The results of existence, uniqueness and stability of positive solutions are proved by using the Banach contrac- tion principle, Guo-Krasnoselskii's xed point theorem and Hyers-Ulam type stability. Two concrete examples are given to illustrate the main results.