RT journal article
T1 A Complex Fractional Mathematical Modelling for the Love Story of Layla and Majnun
A1 Kumar, Pushpendra
A1 Ertuk, V. S.
A1 Murillo Arcila, Marina
A2 Matemáticas
K1 Psychological modelling
K1 Complex variables
K1 Fractional mathematical model
K1 Numerical algorithm
K1 New generalised Caputo type fractional derivative
AB In this article, we provide numerical simulations to show the importance and the effects offractional order derivatives in psychological studies. As it is well-known, complex variablesare more realistic for defining structures in different cases. In this paper, we evidence thatsuch dynamics become more realistic when we use fractional derivatives. We study a nonintegerorder, non-linear mathematical model for defining a love story of Layla and Majnun (acouple in a romantic relationship). We exemplify all necessary practical calculations to studythis serious psychological phenomena. The existence of the unique solution for the givenmodel is exhibited. We use a very recent and strong modified Predictor-Corrector algorithmto evaluate the model structure. Stability of the proposed method is also given. We exemplifythat the given complex fractional model is more realistic and represents reality more closely.The proposed model is very basic, significant, and efficient at introducing distinct naturesby only replacing one control parameter. In this study, we found that in some of the casesthere are stable limit cycles, in some cases periodic behaviours and sometimes transientlychaotic solutions exist which cannot be observed for integer order models at same parametervalues. The principal contribution of this article is to exhibit the importance of non-integerorder derivatives for analysing complex dynamics. The use of complex variables makes thisstudy more effective because they have both magnitude and phase to better explore the loveand can describe different emotions such as coexisting love and hate.
PB Elsevier
SN 0960-0779
YR 2021
FD 2021
LK http://hdl.handle.net/10498/35683
UL http://hdl.handle.net/10498/35683
LA eng
DS Repositorio Institucional de la Universidad de Cádiz
RD 10-may-2026