| Abstract: |
| This work explores the impact of spatiotemporal memory effects, governed by Caputo derivatives, and proportional time delays on the dynamics of fractional physical models. Using a novel transformation method, these models are reformulated into recurrence relations that result in the derivation of convergent series solutions of the Cauchy product type. The results demonstrate that these parameters significantly influence the system`s evolution over time and show a continuous transition from stationary to dynamic states, with the Caputo derivative orders functioning as homotopy parameters in a topological context. Additionally, a detailed graphical analysis highlights the parallel roles of time delays and fractional temporal derivatives, further supporting the view of Caputo derivatives as indicators of memory effects. |
|