C ∗ -ALGEBRA-VALUED SPACES AND THE IMPACT OF MULTI-VALUED FIXED POINT THEOREMS ON HYPERBOLIC TYPE FRACTIONAL DIFFERENTIAL INCLUSIONS

The pursuit of understanding fixed points and their applications has been significantly enhanced through the exploration of multi-valued mappings. This article introduces the concept of multi-valued mappings within C∗-algebra-valued metric spaces. By utilizing the lower bound property, this study extends the Banach, Kannan, and Chatterjea theorems for multi-valued mappings in such spaces (for example see [14]). Moreover, the application aspect is enriched through the provision of an existence result for AB-Caputo partial hyperbolic type fractional differential inclusions. This result enhances the applicability of such inclusions, bridging the gap between theory and application. The paper concludes by offering few open problems that set the stage for future researchers in this field. The results presented here not only generalize numerous findings in the existing literature but also offer new insights into this area of research.