New Existence Results for Nonlinear Fractional Integrodifferential Equations - Lahcen Ibnelazyz; Karim Guida; Khalid Hilal; Said Melliani (Advances in Mathematical Physics)
This paper discusses a boundary value problem of nonlinear fractional integrodifferential equations of order 1<α≤2 and 1<β≤2 and boundary conditions of the form x0=x1=Dcβx1=Dcβx0=0. Some new existence and uniqueness results are proposed by using the fixed point theory. In particular, we make use of the Banach contraction mapping principle and Krasnoselskii’s fixed point theorem under some weak conditions. Moreover, two illustrative examples are studied to support the results.