Abstract
AbstractIn this paper, we study the existence of solutions for a generalized sequential Caputo-type fractional neutral differential inclusion with generalized integral conditions. The used fractional operator has the generalized kernel in the format of $( \vartheta (t)-\vartheta (s)) $
(
ϑ
(
t
)
−
ϑ
(
s
)
)
along with differential operator $\frac{1}{\vartheta '(t)}\,\frac{\mathrm{d}}{\mathrm{d}t}$
1
ϑ
′
(
t
)
d
d
t
. We obtain existence results for two cases of convex-valued and nonconvex-valued multifunctions in two separated sections. We derive our findings by means of the fixed point principles in the context of the set-valued analysis. We give two suitable examples to validate the theoretical results.
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Algebra and Number Theory,Analysis
Reference48 articles.
1. Kisielewicz, M.: Stochastic Differential Inclusions and Applications. Springer, New York (2013)
2. Diethelm, K.A.: The Analysis of Fractional Differential Equations. Springer, Berlin (2010)
3. Kilbas, A.A., Srivastava, H.M., Trujillo, J.J.: Theory and Applications of Fractional Differential Equations. Elsevier, Amsterdam (2006)
4. Lakshmikantham, V., Leela, S., Vasundhara, D.J.: Theory of Fractional Dynamic Systems. Cambridge Academic Publishers, London (2009)
5. Hilfer, R.: Applications of Fractional Calculus in Physics. World Scientific, Singapore (2000)
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