Study of Sturm-Liouville boundary value problems with $ {p} $ -Laplacian by using generalized form of fractional order derivative

Abstract

<abstract><p>This manuscript is related to deriving some necessary and appropriate conditions for qualitative results about a class of Sturm-Liouville (S-L) boundary value problems (BVPs) with the $ p $ -Laplacian operator under a fractional $ \vartheta $ -Caputo type derivative. For the required results, we use Mönch's fixed point theorem with a measuring of non-compactness. Here, it is important to mention that the aforesaid equations belong to a highly significant class of problems that have many of the same properties and applications to solving various problems of dynamics and wave equations theory. For the demonstration of our theoretical results, we provide an example.</p></abstract>