Analytical and Numerical Investigation of Fractional Delay Differential Equations under Relaxed Lipschitz Assumptions (Journal of Nonlinear Modeling and Analysis, 2024)
Fractional delay differential equations constitute a powerful mathematical framework for modeling complex dynamical phenomena exhibitingmemory and delay effects. In this study, we investigate a class of fractionaldelay differential equations incorporating Caputo and Riemann-Liouville fractional derivatives with a delay term. Unlike previous approaches, we establishthe existence and uniqueness of the analytical solution under relaxed Lipschitzconditions on the nonlinear terms, without requiring contraction assumptions.Utilizing Picard iteration techniques, we demonstrate convergence of the numerical method under these Lipschitz conditions, thereby broadening the applicability of our model to a wider range of real-world scenarios. Additionally,numerical tests are conducted to validate the effectiveness and accuracy of theproposed method, further highlighting its utility in practical applications. Ourfindings offer new insights into the modeling and analysis of complex dynamicalsystems, with implications for various scientific and engineering disciplines.