On the existence of solutions for fractional differential inclusions with sum and integral boundary conditions
Section snippets
Introduction and preliminaries
The topic of fractional differential equations is one of the branches of mathematics which has various important applications in many fields as mathematics, physics, chemistry, biology and many other branches of engineering. Many papers have published about fractional differential equations by researchers which apply the fixed point theory in their existence theorems. For instence, one can find a lot of papers in this field (see [1], [2], [3], [4], [5], [10], [11], [12], [13], [14], [15], [17],
Main result
Now, we are ready to prove our main result. Let endowed with the norm . Then, (X, ‖ · ‖) is a Banach space [32].
Lemma 2.1 Given y ∈ X, then the unique solution of the problem
is given by
where
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