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Stability analysis of fractional order modelling of social media addiction

  • *Corresponding author: Pradeep Malik

    *Corresponding author: Pradeep Malik 
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  • In this article, we explored the fractional order mathematical modelling of social media addiction. For the fractional order model of social media addiction, the free equilibrium point $ E_{0} $, endemic equilibrium point $ E_{*} $, and basic reproduction number $ R_0 $ have been found. We discussed the stability analysis of the order model of social media addiction through the next generation matrix and fractional Routh-Hurwitz criterion. We also explained the fractional order mathematical modelling of social media addiction by applying a highly reliable and efficient scheme known as q-Homotopy Analysis Sumudu Transformation Method (q-HASTM). This technique q-HASTM is the hybrid scheme based on q-HAM and Sumudu transform technique. In the end, the numerical simulation of the fractional order model of social media addiction is also explained by using the generalized Adams-Bashforth-Moulton method.

    Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C35.

    Citation:

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  • Figure 1.  Diagram of $ S(t), E(t), A(t), R(t), Q(t) $ w.r.t $ t $ for $ \omega = 1 $

    Figure 2.  Diagram of $ S(t), E(t), A(t), R(t), Q(t) $ w.r.t $ t $ for $ \omega = 0.90 $

    Figure 3.  Diagram of $ S(t), E(t), A(t), R(t), Q(t) $ w.r.t $ t $ for $ \omega = 0.80 $

    Figure 4.  Diagram of $ S(t) $ w.r.t $ t $

    Figure 5.  Diagram of $ E(t) $ w.r.t $ t $

    Figure 6.  Diagram of $ A(t) $ w.r.t $ t $

    Figure 7.  Diagram of $ R(t) $ w.r.t $ t $

    Figure 8.  Diagram of $ Q(t) $ w.r.t $ t $

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