The aim of this work is to study the existence of solutions for nonlocal fractional differential equations inclusions involving ?-Caputo fractional dirivative in Banach space. The proofs are based on the noncompactness measure method. As application, we give an example is given to illustrate the theoretical results.

In this paper, we introduce the fractional Hankel transform in the space of test functions, and we prove some of its properties. In addition, we define this transform in slowly growing distributions space, i.e., in dual space of test functions space. As application, some examples are given to illustrate the theoretical results.

In this research paper, a new concept called ?-?-multivalued contractions is introduced for an ?-admissible mapping in the context of b-metric spaces, which is an extension of the ?-?-contractions originally proposed by Rossafi et al. in 2023. Several fixed point theorems are established, including the ?-admissible ?-?-multivalued theorem of Kanan and the ?-admissible ?-?- multivalued theorem of Riech, all in the framework of b-metric spaces. The applicability of these results is demonstrated using illustrative examples.

The aim of this paper is to introduce the new concept of a multivalued Geraghty type contraction mapping using CG-simulation functions and C-class functions. Additionally, through this type of contraction, we establish fixed point results that generalize several known fixed point results in the literature. As consequences, we arrive at fixed point results endowed with graph. To demonstrate the credibility of our results, we give an example that proves it.