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• W4306293643 abstract "Excessive use of social media is a developing concern in the twenty-first century. This issue needs to be addressed before it has any more significant consequences than what we are currently experiencing. As a preventive technique, advertisements and awareness-raising campaigns about the detrimental impact of digital technologies are used. The application of novel mathematical techniques and terminologies in this field of study will have significant potential to enhance healthy living by preventing certain ailments. This is the most compelling justification for conducting a new study with the most up-to-date techniques at our disposal. This study investigates clear and concise transmission in order to generate a deterministic mathematical model of social media addiction <math xmlns=http://www.w3.org/1998/Math/MathML id=M1> <mi mathvariant=double-struck>S</mi> <mi mathvariant=double-struck>M</mi> <mi mathvariant=double-struck>A</mi> </math> using the fractal-fractional (FF) derivative operator. Also, the analysis of the <math xmlns=http://www.w3.org/1998/Math/MathML id=M2> <mi mathvariant=double-struck>S</mi> <mi mathvariant=double-struck>M</mi> <mi mathvariant=double-struck>A</mi> </math> model in terms of the invariant domain, the existence of a positive invariant solution, and equilibria assumptions are stated in a detailed manner. Besides that, the basic reproduction number <math xmlns=http://www.w3.org/1998/Math/MathML id=M3> <msub> <mrow> <mi>ℝ</mi> </mrow> <mrow> <mn>0</mn> </mrow> </msub> <mo><</mo> <mn>1</mn> </math> is computed, demonstrating that the proposed methodology is more efficacious. The Atangana-Baleanu FF differential operators are recently defined in FF differential operators that are applied to characterize the <math xmlns=http://www.w3.org/1998/Math/MathML id=M4> <mi mathvariant=double-struck>S</mi> <mi mathvariant=double-struck>M</mi> <mi mathvariant=double-struck>A</mi> </math> model’s mathematical algorithm. We investigated the numerical behaviour of the <math xmlns=http://www.w3.org/1998/Math/MathML id=M5> <mi mathvariant=double-struck>S</mi> <mi mathvariant=double-struck>M</mi> <mi mathvariant=double-struck>A</mi> </math> in three ways: (i) changing the fractional-order <math xmlns=http://www.w3.org/1998/Math/MathML id=M6> <mfenced open=( close=) separators=|> <mrow> <mi>α</mi> </mrow> </mfenced> </math> as well as the fractal-dimension <math xmlns=http://www.w3.org/1998/Math/MathML id=M7> <mfenced open=( close=) separators=|> <mrow> <mi>℘</mi> </mrow> </mfenced> </math> ; (ii) changing <math xmlns=http://www.w3.org/1998/Math/MathML id=M8> <mi>α</mi> </math> while keeping <math xmlns=http://www.w3.org/1998/Math/MathML id=M9> <mi>℘</mi> </math> constant; and (iii) changing <math xmlns=http://www.w3.org/1998/Math/MathML id=M10> <mi>℘</mi> </math> while keeping <math xmlns=http://www.w3.org/1998/Math/MathML id=M11> <mi>α</mi> </math> constant. Our examined visualizations and simulation studies using MATLAB for the numerical modelling of the aforementioned system showed that the novel developed Atangana-Baleanu FF differential operators produce remarkable results when compared to the classical frame." @default.
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• W4306293643 date "2022-10-15" @default.
• W4306293643 modified "2023-09-26" @default.
• W4306293643 title "Nonlinear dynamics of the media addiction model using the fractal-fractional derivative technique" @default.
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• W4306293643 doi "https://doi.org/10.1155/2022/2140649" @default.
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