Solution of fractional oxygen diffusion problem having without singular kernel

Alkahtani, Badr Saad T.; Algahtani, Obaid; Dubey, Ravi Shanker; Goswami, Pranay

doi:10.22436/jnsa.010.01.28

Cited by 11 publications

(13 citation statements)

References 13 publications

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“…Uniqueness of the coupled solutions. In this section, we show that the solutions of equation (10) and (11) are unique. To prove the uniqueness, we have considered that there is an another solution for equation (10), then…”

mentioning

confidence: 95%

“…To define the existence of the coupled solution we use the Fixed-Point theorem. In this way first we transform the equations (10) and (11) in to integral equation as follows…”

mentioning

confidence: 99%

“…Hence on the behalf of equation 45and (46) we can say that equation (10) and (11) have unique solution.…”

mentioning

confidence: 99%

“…Stability analysis. In this section we describe the fractional mathematical model of the patient diabetes and it's complication defined in equation (10) and (11). As we talk about the fractional model defined in equation (10) and (11).…”

mentioning

confidence: 99%

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Mathematical model of diabetes and its complication involving fractional operator without singular kernal

Dubey¹,

Goswami²

2021

DCDS-S

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Diabetes is one of the burning issues of the whole world. It effected the world population rapidly. According to the WHO approx 415 million people are living with diabetes in the world and this figure is expected to rise up to 642 million by 2040. World various organizations raise their voice against the dire facts about the increasing graph of diabetes and its complicated patients. In this paper authors define the fractional model of diabetes and its complications involving to fractional operator with exponential kernel. The authors discuss the existence of the solution by using fixed point theorem and also show the uniqueness of the solution. To validate the model's efficiency the authors provided numerical simulation by using HPM. To strengthen the model the results have been presented in the form of graphs.

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mentioning

confidence: 95%

“…To define the existence of the coupled solution we use the Fixed-Point theorem. In this way first we transform the equations (10) and (11) in to integral equation as follows…”

mentioning

confidence: 99%

“…Hence on the behalf of equation 45and (46) we can say that equation (10) and (11) have unique solution.…”

mentioning

confidence: 99%

mentioning

confidence: 99%

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Mathematical model of diabetes and its complication involving fractional operator without singular kernal

Dubey¹,

Goswami²

2021

DCDS-S

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“…Liapis et al in [14] proposed an orthogonal collocation method for solving the PDE of the diffusion of oxygen in absorbing tissue. In [15], the authors applied the Caputo-Fabrizio fractional derivative to the oxygen diffu-sion equation, the authors obtained the solution using an iterative method. Another interesting applications have been investigated in [16][17][18].…”

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confidence: 99%

Modelling the oxygen diffusion equation within the scope of fractional calculus

Fabian¹,

Gómez-Aguilar²,

Atangana³

2019

THERM SCI

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The diffusion of oxygen into human body with simultaneous absorption is an important problem and it is of great importance in medical applications. This problem can be formulated in two stages. At the first stage, the absorption of oxygen at the surface of the medium is constant and an another stage considering the moving boundary problem of oxygen absorbed by the human body. In this paper we obtain analytical solutions for the oxygen diffusion equation considering the Liouville-Caputo, Atangana-Baleanu-Caputo, fractional conformable derivative in the Liouville-Caputo sense, and Atangana-Koca-Caputo fractionalorder derivatives. Numerical simulations were obtained for different values of the fractional order.

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A study of the fractional‐order mathematical model of diabetes and its resulting complications

Srivástava

Dubey

Jain

2019

Math Methods in App Sciences

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Diabetes is a worldwide problem that affects one of every 11 persons nowadays. The IDF Diabetes Atlas (Eighth edition, 2017) states that approximately 415 million people in the world are living with the disease and that this number will rise to 629 million by the year 2045. It is a very serious problem of the world. A major part of the world population is affected by this disease and its resulting complications. In this paper, we propose to investigate a fractional-order model of diabetes and its resulting complications. The mathematical model's parameters define the population of diabetic patients and those who are diabetic with complications at a given time t. We have also discussed the existence, uniqueness, and stability of the fractional-order model, which we consider here. We make use of the homotopy decomposition method (HDM) in order to solve the problem. KEYWORDSdiabetes and its resulting complications, existence, fractional calculus, fractional-order modeling, homotopy decomposition method (HDM), uniqueness and stability

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Solution of fractional oxygen diffusion problem having without singular kernel

Cited by 11 publications

References 13 publications

Mathematical model of diabetes and its complication involving fractional operator without singular kernal

Mathematical model of diabetes and its complication involving fractional operator without singular kernal

Modelling the oxygen diffusion equation within the scope of fractional calculus

A study of the fractional‐order mathematical model of diabetes and its resulting complications

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