A study of fractional differential equations and inclusions involving generalized Caputo-type derivative equipped with generalized fractional integral boundary conditions

On a fractional differential inclusion involving a generalized Caputo type derivative with certain fractional integral boundary conditions

“…Remark 3.4. A similar existence result to the one in Corollary 3.3 may be found in [10], namely Theorem 4.2. Its proof is performed by using the set-valued contraction principle.…”

“…Example 3.5. As an application of our above result one may consider the following example taken from [10]. Consider the following problem…”

“…It is worth to mention that the approach in [10], apart from the requirement that the values of F(., .) are compact, does not provides a priori bounds as in (3.7).…”

“…dt and F : [0, T ] × R → P(R) is a set-valued map. In a recent paper [10], problem (1.1)-(1.2) was studied and two existence results for this problem are provided taking into account the situations when the values of the setvalued map F are convex and nonconvex. The results in [10] are obtained by using fixed point techniques.…”

“…Our goal is to continue the study in [10]. Namely, our aim is twofold: on one hand, we show that Filippov's technique [11] may be used in order to obtain the existence of solutions for problem (1.1)-(1.2).…”