TY - JOUR
T1 - Analytical and Numerical Investigation of Fractional Delay Differential Equations under Relaxed Lipschitz Assumptions
AU - Segni , Sami
AU - Guebbai , Hamza
AU - Dida , Ridha
JO - Journal of Nonlinear Modeling and Analysis
VL - 4
SP - 1245
EP - 1254
PY - 2024
DA - 2024/12
SN - 6
DO - http://doi.org/10.12150/jnma.2024.1245
UR - https://global-sci.org/intro/article_detail/jnma/23684.html
KW - Fractional differential equation, delay term, Picard method, numerical integration.
AB - <p style="text-align: justify;">Fractional delay differential equations constitute a powerful mathematical framework for modeling complex dynamical phenomena exhibiting
memory and delay effects. In this study, we investigate a class of fractional
delay differential equations incorporating Caputo and Riemann-Liouville fractional derivatives with a delay term. Unlike previous approaches, we establish
the existence and uniqueness of the analytical solution under relaxed Lipschitz
conditions 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 the
proposed method, further highlighting its utility in practical applications. Our
findings offer new insights into the modeling and analysis of complex dynamical
systems, with implications for various scientific and engineering disciplines.</p>