In this paper we prove some new results on SturmLiouville abstract problems of the second order dierential equations of elliptic type in a new non-commutative framework. We study the case when the second member belongs to a Sobolov space. Existence, uniqueness and optimal regularity of the strict solution are proved. This paper is naturally the continuation of the ones studied by Cheggag et al in the commutative case. We also give an example to which our theory applies.
In this paper, we study the existence of solutions for a coupled system of fractional differential equations with nonlocal integro multi point boundary conditions by using the Laplacian operator and the Hilfer derivatives. The presented results are obtained by the fixed point theorems of Krasnoselskii. An illustrative example is presented at the end to show the applicability of the obtained results. To the best of our knowledge, this is the first time where such problem is considered.
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