Pratibha Verma, Wojciech Sumelka
Institute of Structural Analysis, Poznan University of Technology,
Piotrowo 5 Street, Poznan 60-965, Poland
Received 18 June, 2025; accepted in revised form 30 June, 2025
Abstract: The primary purpose of this work is to study complex-order differential equations. In particular, we explore results involving Hilfer fractional derivatives of complex order. We develop existence and uniqueness results for the proposed problem using the Schauder Fixed Point Theorem. Furthermore, we investigate the stability of the Hyers-Ulam solution under suitable conditions. In addition, we present an example to illustrate the applicability of the results obtained. These findings lay a foundation for future research on advanced fractional models with applications in science and engineering, particularly in systems exhibiting memory, hereditary properties, or complex dynamic behavior. The developed framework may also guide the formulation of numerical methods and stability analysis in practical problems ranging from viscoelastic materials to anomalous diffusion and control theory.
Keywords: Hyers–Ulam Stability, Caputo derivative, ψ-Hilfer Fractional Derivative, Com-
plex Order Fractional Derivatives, Nonlinear Fractional Differential Equations, Fixed Point Methods, Existence and Uniqueness Results.
Mathematics Subject Classification: 26E30, 34M10, 34A08, 30D35, 47H10