Comparative study of tuberculosis infection by using general fractional derivative

Manvendra Narayan Mishra; Faten Aldosari; Manvendra Narayan Mishra; Faten Aldosari

doi:10.3934/math.2025058

AIMS Mathematics

2025, Volume 10, Issue 1: 1224-1247. doi: 10.3934/math.2025058

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Research article

Comparative study of tuberculosis infection by using general fractional derivative

Manvendra Narayan Mishra ^{1
,
,},
Faten Aldosari ²

1.
Department of Mathematics, Suresh Gyan Vihar University, Jaipur, Rajasthan, India
2.
Department of Mathematics, College of Science, Shaqra University, P.O. Box 15572, Shaqra 11961, Saudi Arabia

Received: 14 September 2024 Revised: 06 December 2024 Accepted: 17 December 2024 Published: 21 January 2025
MSC : 26A33, 92B05, 92C60

The current study examined the general fractional derivative of the fractional order in the context of an incomplete treatment of tuberculosis (TB). Utilizing the fixed-point technique and nonlinear analysis, we arrived at certain theoretical conclusions on the existence and stability of the solution. The well-known Laplace transform method was used to calculate the arithmetic output of the model under consideration. This approach depends upon an elementary principle of fractional calculus. For each case of general fractional derivative, numerical simulation was also provided, each one linked with a particular fractional order in (0, 1).
- TB,
- tuberculosis disease,
- generalized derivative,
- fractional operator,
- fixed point condition,
- Laplace transform
Citation: Manvendra Narayan Mishra, Faten Aldosari. Comparative study of tuberculosis infection by using general fractional derivative[J]. AIMS Mathematics, 2025, 10(1): 1224-1247. doi: 10.3934/math.2025058

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Abstract

The current study examined the general fractional derivative of the fractional order in the context of an incomplete treatment of tuberculosis (TB). Utilizing the fixed-point technique and nonlinear analysis, we arrived at certain theoretical conclusions on the existence and stability of the solution. The well-known Laplace transform method was used to calculate the arithmetic output of the model under consideration. This approach depends upon an elementary principle of fractional calculus. For each case of general fractional derivative, numerical simulation was also provided, each one linked with a particular fractional order in (0, 1).

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