Heat and mass transport of differential type fluid with non-integer order time-fractional Caputo derivatives

Imran, Muhammad; Khan, İlyas; Ahmad, Mushtaq; Nazar, Mudassar

doi:10.1016/j.molliq.2016.11.095

Cited by 113 publications

(33 citation statements)

References 14 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…As long as computer science is related, the models depending upon fractional-order derivatives are found to be useful to understand the ways for the spread of computer bugs and viruses [10]. Imran et al in [11] proved the better performance of Caputo fractional order derivatives to analyze the fluid flow problems with regard to non-dimensional temperature, concentration, and velocity fields.…”

Section: Introductionmentioning

confidence: 99%

Using Shehu integral transform to solve fractional order Caputo type initial value problems

Qureshi¹,

Kumar²

2019

J. Appl. Math. Comput. Mech.

View full text Add to dashboard Cite

In the present research analysis, linear fractional order ordinary differential equations with some defined condition (s) have been solved under the Caputo differential operator having order α > 0 via the Shehu integral transform technique. In this regard, we have presented the proof of finding the Shehu transform for a classical nth order integral of a piecewise continuous with an exponential order function which leads towards devising a theorem to yield exact analytical solutions of the problems under investigation. Varying fractional types of problems are solved whose exact solutions can be compared with solutions obtained through existing transformation techniques including Laplace and Natural transforms.

show abstract

Section: Introductionmentioning

confidence: 99%

Using Shehu integral transform to solve fractional order Caputo type initial value problems

Qureshi¹,

Kumar²

2019

J. Appl. Math. Comput. Mech.

View full text Add to dashboard Cite

show abstract

“…Recently, Imran et al [22] studied the comparison approach between Caputo-Fabrizio and Atangana-Baleanu fractional derivative and found that Atangana-Baleanu fractional derivative is excellent in exhibiting the memory effect in fluid flow problems. Some recent studies related to the applications of modern techniques of fractional derivatives can be seen [23][24][25][26][27][28][29][30][31][32][33]. Due to vast applications of fractional derivatives, applied this technique to multilayered tissues of breast cancer and found semi exact solutions with and found some useful conclusion for experts to treat cancer cells with suitable amount of heat source and have compared the results to see the memory effect of temperature function.…”

Section: Introductionmentioning

confidence: 99%

Fractional Mechanism with Power Law (Singular) and Exponential (Non-singular) Kernels and Its Applications in Bio Heat Transfer Model

Asjad¹

2019

IJHT

View full text Add to dashboard Cite

This study deals with breast cancer therapy with fractional derivative in porous medium. The classical model of energy balance equation can be generalized to some fractional derivatives namely, Caputo (C) with singular kernel and Atangana-Baleanu (ABC) with non-singular kernel. We have found the semi exact solutions of initial value problem via Laplace transform. Hyperthermia technique named as a moderate method for the treatment of breast cancer. Graphical illustration is provided for numerical values of embedded parameters with the help of MATHCAD software. As a result, a steady-state time required the therapeutic temperature point to get the death of tumor cell has been computed. A comparison has also been drawn between the solutions of fractional models with fractional derivatives and found that Atangana-Baleanu fractional model is well suited in exhibiting the memory effect of the temperature function. The findings of this research may serve the advantage that it is affordable and important in clinical or medical practice.

show abstract

“…Khan et al have discussed effects of magnetic field on molybdenum disulfide nanofluids in mixed convection flow inside a channel filled with a saturated porous medium. Most researches are conducted in closely related manner and could be found in …”

Section: Introductionmentioning

confidence: 99%

“…Most researches are conducted in closely related manner and could be found in. [27][28][29][30][31][32][33][34][35][36] The numerical or analytical solution of all above examinations is acquired accepting the fluid stream accelerated exponentially or oscillatory. Be that as it may, there exist a few issues of physical interest, which may accelerate instantly.…”

mentioning

confidence: 99%

Thermal radiation and inclined magnetic field effects on MHD flow past a linearly accelerated inclined plate in a porous medium with variable temperature

Endalew

Nayak

2018

Heat Trans. Asian Res.

View full text Add to dashboard Cite

An analysis of unsteady MHD natural convective flow, transfer of mass, and radiation past linearly accelerated slanted plate inserted in an immersed permeable medium with uniform permeability, variable temperature, and concentration within the sight of a slanted magnetic field has been done. The novelty of the current examination is to analyze the effect of a slanted magnetic field on the flow phenomena with heat source/sink and destructive reaction for linearly accelerated slanted plate. The governing equations have been solved by using Laplace transform strategy. The estimations of flow velocity, concentration, and temperature are exhibited graphically, while local skin friction, mass, and heat transfer rates are put on view in tabular form for different values of relevant stream parameters. It is fascinating to observe that the raise of inclination angle of an applied magnetic field diminishes both velocity profiles and local skin friction.

show abstract

Heat and mass transport of differential type fluid with non-integer order time-fractional Caputo derivatives

Cited by 113 publications

References 14 publications

Using Shehu integral transform to solve fractional order Caputo type initial value problems

Using Shehu integral transform to solve fractional order Caputo type initial value problems

Fractional Mechanism with Power Law (Singular) and Exponential (Non-singular) Kernels and Its Applications in Bio Heat Transfer Model

Thermal radiation and inclined magnetic field effects on MHD flow past a linearly accelerated inclined plate in a porous medium with variable temperature

Contact Info

Product

Resources

About