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Time-Fractional Differential Equations with Variable Order using RDTM and ADM: Application to Infectious-Disease Model

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Abstract

From the current scenario it is well known that the most of the engineering problem leads to the mathematical model with different concept. Associated with these phenomena, the present investigation gathers some physical interpretation of different model that leads to couple nonlinear time fractional differential equation encompass with variable order within certain domain relating to the physical significance of the corresponding problem. The system of equations is based upon Caputo-type fractional differential equation in particular cases. The crux of this investigation is that the use of various solution approach for the modeled problems such as “Reduced Differential Transform Method” and “Adomian Decomposition Method”. Finally, the aforesaid methodologies are also applicable for the infectious diseases model and verified in particular case of integral order with an earlier investigation.

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No data is used.

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Abbreviations

\(s(t)\) :

The number of uninfected and no immunity computers that are susceptible at any given time t

\(a(t)\) :

At any given time t, new or ancient antidotal computers in use

\(e(t)\) :

The number of exposed computers that are susceptible to infection at any given time t

\(i(t)\) :

The number of infected computers that must be cured at any given time t

\(q(t)\) :

At any given time t, infected computers quarantined

\(r(t)\) :

At a time t, uninfected computers with temporary immunity

\(B\) :

Rate at which the new computers associated to network system i.e. Birth rate

\(\mu\) :

Rate of death when computers are affected other than virus attack

\(k_{1}\) :

Rate of death when computers are affected by virus attack

\(\beta\) :

Transmission rate when susceptible computers contact with infected ones

\(\alpha\) :

The rate at which antidotal process begins with the susceptible computers

\(\phi_{1}\) :

Rate of virus attack

\(\phi_{2}\) :

Rate of recovery by antidotal computers

\(\gamma\) :

Rate of coefficient of exposed class (E to I)

\(\sigma_{1}\) :

Infectious class (I to R)

\(\sigma_{2}\) :

Infectious class (I to Q)

\(\delta\) :

Quarantine class (Q to R) and its rate

\(\eta\) :

Recovery class (R to S) and its rate

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Authors and Affiliations

  1. Department of Mathematics, Siksha ‘O’ Anusandhan Deemed to Be University, Bhubaneswar, Odisha, 751030, India

    S. N. Mohapatra, S. R. Mishra & P. Jena

Authors
  1. S. N. Mohapatra
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  2. S. R. Mishra
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  3. P. Jena
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Contributions

All the authors have equally contributed to complete the manuscript, i.e. SNM has completed the introduction section and checked the similarity with grammar, PJ has formulated the problem, simulated the semi-analytical results and completed the draft, SRM has corrected the results and completed the discussion section.

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Correspondence to P. Jena.

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Mohapatra, S.N., Mishra, S.R. & Jena, P. Time-Fractional Differential Equations with Variable Order using RDTM and ADM: Application to Infectious-Disease Model. Int. J. Appl. Comput. Math 8, 138 (2022). https://doi.org/10.1007/s40819-022-01332-2

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