Fractional Meijer <i>K</i> ‐Transformation of Generalized Functions

ABSTRACT In this study, we introduce and explore the fractional powers of Meijer ‐transformation of order (where ) with a specific parameter , applying them to certain generalized functions. We examine the properties of these fractional powers in detail, establishing a theoretical foundation for their behavior. As a practical application of our results, we demonstrate how these concepts can be utilized to solve partial differential equations involving Kepinski‐type operator , thereby illustrating the theoretical results in a tangible context.