Analytical Solution for the Differential Equation Containing Generalized Fractional Derivative Operators and Mittag-Leffler-Type Function

Chaurasia, V. B. L.; Dubey, Ravi Shanker

doi:10.5402/2011/682381

Cited by 11 publications

(6 citation statements)

References 11 publications

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“…Many researchers like Caputo, Miller, Ross, Kilbas, Srivastava, Trujillo, etc give lots of knowledge to know more about the fractional calculus and its application. In the path of knowledge they have contributed a lot (see [13], [16], [17], [18], [23], [26], [29] and [31]). Fractional calculus is also having a great importance in mathematical modeling to define the real world problems.…”

Section: Preventing Ways Of Diabetesmentioning

confidence: 99%

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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Section: Preventing Ways Of Diabetesmentioning

confidence: 99%

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

Dubey¹,

Goswami²

2021

DCDS-S

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“…Homogeneous beam's transverse vibrations are controlled by fractional single fourth-order parabolic partial differential equations (PDEs). Such problem types occur in viscoelastic and inelastic flow mathematical modeling, layer deflection theories, and beam deformation [1][2][3][4][5][6][7][8][9][10][11][12]. Analyses of these problems have taken several physicist's and mathematician's attention [13][14][15].…”

Section: Introductionmentioning

confidence: 99%

Numerical Analysis of Fractional-Order Parabolic Equations via Elzaki Transform

Naeem

Azhar

Zidan

et al. 2021

Journal of Function Spaces

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This research article is dedicated to solving fractional-order parabolic equations, using an innovative analytical technique. The Adomian decomposition method is well supported by Elzaki transformation to establish closed-form solutions for targeted problems. The procedure is simple, attractive, and preferred over other methods because it provides a closed-form solution for the given problems. The solution graphs are plotted for both integer and fractional-order, which shows that the obtained results are in good contact with problems’ exact solution. It is also observed that the solution of fractional-order problems is convergent to the integer-order problem. Moreover, the validity of the proposed method is analyzed by considering some numerical examples. The theory of the suggested approach is fully supported by the obtained results for the given problems. In conclusion, the present method is a straightforward and accurate analytical technique that can solve other fractional-order partial differential equations.

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“…It is capable of modeling and analyzing linear as well as complex phenomena of engineering and applied sciences. In modern time, fractional calculus plays very essential role in such fields as (for example) biology, geophysics, biomedical engineering, fluid dynamics, electricity, and mechanics (see other works()). It has thus become a very efficient tool to describe significant models of the natural phenomena.…”

Section: An Introductory Overview Of Fractional Calculusmentioning

confidence: 99%

“…Many mathematical scientists and researchers have been working in this field, such as (for example) those who are included in the list of our citations, by introducing various fractional calculus models (see other studies()).…”

Section: An Introductory Overview Of Fractional Calculusmentioning

confidence: 99%

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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Analytical Solution for the Differential Equation Containing Generalized Fractional Derivative Operators and Mittag-Leffler-Type Function

Cited by 11 publications

References 11 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

Numerical Analysis of Fractional-Order Parabolic Equations via Elzaki Transform

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

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