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Dynamics of Mental Disorders Using ψ- Hilfer Fractional Derivative |
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PP: 161-175 |
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doi:10.18576/pfda/110112
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Author(s) |
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Nandhini Mohankumar,
Lavanya Rajagopal,
Juan J. Nieto,
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Abstract |
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| Around the globe, fear and anxiety are being triggered by the COVID-19 pandemic and lockdown, the stress induced by this issue has resulted in a negative impact on people’s mental health and psychosocial development. The repercussions of this epidemic on one’s mental health have not received much focus in the society. In this paper, We formulate a mathematical model to investigate the dynamic behavior of mental disorders induced by the COVID-19 pandemic. The peculiar behavior of the transition between mental disorders, coexistence, and their influence on people’s mental health are studied in the model. A fixed-point analysis is used to determine the existence and uniqueness of the solution with ψ-Hilfer fractional derivatives. Adomian decomposition method paired with Laplace integral transform is employed to obtain the solution. The numerical simulation of the fractional model is investigated through Caputo fractional derivative and the graphical representation are depicted for different fractional orders. Further, we compare our results with reported real data against the simulated data of the depressed population for the consecutive 7 years in India. This research is intended towards improving a strong knowledge about psychological disorders in an effort to enhance mental wellness.
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