Toward solving fractional differential equations via solving ordinary differential equations

Jalil, Ahmed F. Abdel; Khudair, Ayad R.

doi:10.1007/s40314-021-01744-8

Cited by 15 publications

(6 citation statements)

References 39 publications

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“…Refs. [57] , [58] , [59] , [60] , [61] , [62] , [63] , [64] ). However, to give a complete picture of the stability analysis in the previous section, we will use the fractional Euler method (FEM) 37 to solve the model numerically.…”

Section: Numerical Simulationsmentioning

confidence: 99%

Studying of COVID-19 fractional model: Stability analysis

Khalaf

Kadhim

Khudair

2023

Partial Differential Equations in Applied Mathematics

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Section: Numerical Simulationsmentioning

confidence: 99%

Studying of COVID-19 fractional model: Stability analysis

Khalaf

Kadhim

Khudair

2023

Partial Differential Equations in Applied Mathematics

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“…The optimal control theory is applied in a variety of fields, such as the design of therapy [22], the optimal control of the disease among animals [23], and the best tuberculosis prevention strategy [24,25], in order to improve control. Additionally, the theory and application of fractional calculus have been extensively utilized in order to model dynamic processes in a variety of fields, including but not limited to the fields of science and engineering [26,27,28]. Fractional order derivatives have an important property known as the memory effect.…”

Section: Issn: 0067-2904mentioning

confidence: 99%

Design of Optimal Control for the In-host Tuberculosis Fractional Model

Khalaf,

Kadhim

2023

Iraqi Journal of Science

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In this article, we investigate a mathematical fractional model of tuberculosis that takes into account vaccination as a possible way to treat the disease. We use an in-host tuberculosis fractional model that shows how Macrophages and Mycobacterium tuberculosis interact to knowledge of how vaccination treatments affect macrophages that have not been infected. The existence of optimal control is proven. The Hamiltonian function and the maximum principle of the Pontryagin are used to describe the optimal control. In addition, we use the theory of optimal control to develop an algorithm that leads to choosing the best vaccination plan. The best numerical solutions have been discovered using the forward and backward fractional Euler method.

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“…Some scholar investigate the impact of self-isolation, quarantine, and contact tracing on the stopping and control of the COVID-19 pandemic using data from the New York population [25] . On the other hand, fractional differential equations play a fundamental role in the distribution of the COVID-19 pandemic [26] , [27] , so there are numerous methods to solve them [28] , [29] , [30] , [31] .…”

Section: Introductionmentioning

confidence: 99%