Existence of Solutions to Fractional Mixed Integrodifferential Equations with Nonlocal Initial Condition
نویسندگان
چکیده
We study the existence and uniqueness theorem for the nonlinear fractional mixed Volterra-Fredholm integrodifferential equation with nonlocal initial condition dx t /dt f t, x t , ∫ t 0 k t, s, x s ds, ∫1 0 h t, s, x s ds , x 0 ∫1 0 g s x s ds, where t ∈ 0, 1 , 0 < α < 1, and f is a given function. We point out that such a kind of initial conditions or nonlocal restrictions could play an interesting role in the applications of the mentioned model. The results obtainded are applied to an example.
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