A Class of Nonlinear Boundary Value Problems for an Arbitrary Fractional-Order Differential Equation with the Riemann-Stieltjes Functional Integral and Infinite-Point Boundary Conditions

Srivástava, H. M.; El-Sayed, A. M. A.; Gaafar, Fatma M.

doi:10.3390/sym10100508

Cited by 27 publications

(23 citation statements)

References 28 publications

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“…The main advantages of these operator is the freedom of choice of the function ψ and its merge and acquire the properties of the aforementioned fractional operators. Results based on these setting can be found in [18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34]. The Ulam-Hyers stability point of view, is the vital and special type of stability that attracts many researchers in the field of mathematical analysis.…”

Section: Introductionmentioning

confidence: 99%

Stability Results for Implicit Fractional Pantograph Differential Equations via ϕ-Hilfer Fractional Derivative with a Nonlocal Riemann-Liouville Fractional Integral Condition

et al. 2020

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This paper presents a class of implicit pantograph fractional differential equation with more general Riemann-Liouville fractional integral condition. A certain class of generalized fractional derivative is used to set the problem. The existence and uniqueness of the problem is obtained using Schaefer’s and Banach fixed point theorems. In addition, the Ulam-Hyers and generalized Ulam-Hyers stability of the problem are established. Finally, some examples are given to illustrative the results.

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Section: Introductionmentioning

confidence: 99%

Stability Results for Implicit Fractional Pantograph Differential Equations via ϕ-Hilfer Fractional Derivative with a Nonlocal Riemann-Liouville Fractional Integral Condition

et al. 2020

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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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“…Hameed et al [24] examined the fractional order second grade fluid peristaltic transport in a vertical cylinder. A variety of numerical techniques have been used to find solutions to the classical models [25][26][27][28][29][30], and these techniques have been further combined to find solutions for fractional order problems.…”

Section: Introductionmentioning

confidence: 99%

Fractional Order Forced Convection Carbon Nanotube Nanofluid Flow Passing Over a Thin Needle

et al. 2019

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In the fields of fluid dynamics and mechanical engineering, most nanofluids are generally not linear in character, and the fractional order model is the most suitable model for representing such phenomena rather than other traditional approaches. The forced convection fractional order boundary layer flow comprising single-wall carbon nanotubes (SWCNTs) and multiple-wall carbon nanotubes (MWCNTs) with variable wall temperatures passing over a needle was examined. The numerical solutions for the similarity equations were obtained for the integer and fractional values by applying the Adams-type predictor corrector method. A comparison of the SWCNTs and MWCNTs for the classical and fractional schemes was investigated. The classical and fractional order impact of the physical parameters such as skin fraction and Nusselt number are presented physically and numerically. It was observed that the impact of the physical parameters over the momentum and thermal boundary layers in the classical model were limited; however, while utilizing the fractional model, the impact of the parameters varied at different intervals.

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A Class of Nonlinear Boundary Value Problems for an Arbitrary Fractional-Order Differential Equation with the Riemann-Stieltjes Functional Integral and Infinite-Point Boundary Conditions

Cited by 27 publications

References 28 publications

Stability Results for Implicit Fractional Pantograph Differential Equations via ϕ-Hilfer Fractional Derivative with a Nonlocal Riemann-Liouville Fractional Integral Condition

Stability Results for Implicit Fractional Pantograph Differential Equations via ϕ-Hilfer Fractional Derivative with a Nonlocal Riemann-Liouville Fractional Integral Condition

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

Fractional Order Forced Convection Carbon Nanotube Nanofluid Flow Passing Over a Thin Needle

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