Abstract
In this paper, we investigated the system of fractional differential equations with integral boundary conditions. By using a fixed point theorem in the Banach spaces, we get the existence of solutions for the fractional differential system. By constructing iterative sequences for any given initial point in space, we can approximate this solution. As an application, an example is presented to illustrate our main results.
Highlights
The fractional differential equations attracted many people’s attention, and they have many applications in different fields of science and biology
We investigated the system of fractional differential equations with integral boundary conditions
In [7], Wang et al studied the existence of solutions for the following system of nonlinear fractional differential equations: Dαu (t) = f (t, V (t)), DβV (t) = g (t, u (t)), u (0) = V (0) = 0, (2)
Summary
The fractional differential equations attracted many people’s attention, and they have many applications in different fields of science and biology. In [7], Wang et al studied the existence of solutions for the following system of nonlinear fractional differential equations: Dαu (t) = f (t, V (t)) , DβV (t) = g (t, u (t)) , u (0) = V (0) = 0,. In [8], Yang studied the existence of solutions for the following system of nonlinear fractional differential equations: Dαu (t) = a (t) f (t, V (t)) , DβV (t) = b (t) g (t, u (t)) , u (0) = V (0) = 0, (3). In [10], Yang et al studied the existence of solutions for the following system of fractional differential equations with integral boundary conditions:. We know 0 < θ4 ≤ θ1 < 1, 0 < θ5 ≤ θ2 < 1, 0 < θ6 ≤ θ3 < 1
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