Author:
Lachouri Adel, ,Abdo Mohammed S.,Ardjouni Abdelouaheb,Abdalla Bahaaeldin,Abdeljawad Thabet, , , ,
Abstract
<abstract><p>In the present paper, we extend and develop a qualitative analysis for a class of nonlinear fractional inclusion problems subjected to nonlocal integral boundary conditions (nonlocal IBC) under the $ \varphi $-Hilfer operator. Both claims of convex valued and nonconvex valued right-hand sides are investigated. The obtained existence results of the proposed problem are new in the frame of a $ \varphi $-Hilfer fractional derivative with nonlocal IBC, which are derived via the fixed point theorems (FPT's) for set-valued analysis. Eventually, we give some illustrative examples for the acquired results.</p></abstract>
Publisher
American Institute of Mathematical Sciences (AIMS)
Reference54 articles.
1. K. Diethelm, The analysis of fractional differential equations, Lecture Notes in Mathematics, Springer-verlag, Berlin, Heidelberg, 2010. doi: 10.1007/978-3-642-14574-2.
2. A. A. Kilbas, H. M. Srivastava, J. J. Trujillo, Theory and applications of fractional differential equations, Elsevier Science B. V., Amsterdam, 2006. doi: 10.1016/S0304-0208(06)80001-0.
3. V. Lakshmikantham, S. Leela, J. V. Devi, Theory of fractional dynamic systems, Cambridge, UK: Cambridge Scientific Publishers, 2009.
4. I. Podlubny, Fractional differential equations, San Diego: Academic Press, 1999.
5. D. Baleanu, S. Etemad, S. Rezapour, A hybrid Caputo fractional modeling for thermostat with hybrid boundary value conditions, Bound. Value Probl., 2020 (2020), 64. doi: 10.1186/s13661-020-01361-0.
Cited by
2 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献