Numerical solution of two-dimensional fractional order Volterra integro-differential equations

Ahsan, Sumbal; Nawaz, Rashid; Akbar, M. Ali; Nisar, Kottakkaran Sooppy; Abualnaja, Kholod M.; Mahmoud, Emad E.; Abdel‐Aty, Abdel‐Haleem

doi:10.1063/5.0032636

Cited by 8 publications

(2 citation statements)

References 30 publications

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“…In addition, singularity is also generated at the boundary of the domain. So, execution of computational approaches such as finite Frontiers in Physics frontiersin.org volume, finite element, and finite difference are considered to be the fittest to attain the approximate solution [26][27][28][29]. Among this, the most flexible and rapid technique is the finite element scheme.…”

Section: Mathematical Modelingmentioning

confidence: 99%

RETRACTED: Mixed convective heat transfer in a power-law fluid in a square enclosure: Higher order finite element solutions

et al. 2023

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Incorporation of momentum gradients produced due to inertial motion of the lid along with the presence of temperature differences in the configuration make the physical problem more significant. The joint variation of momentum and thermal diffusion in diversified natural liquids is recognized as mixed convection. Valuable attention has been received by such a phenomenon in different areas of science and technology such as in wind current–based solar receivers, electronic instruments, control of emergency shutdown in reactors, thermal exchangers, oceanic currents, control of atmospheric pollution, and so on. So, the main focus is to contemplate hydrothermal characteristics of a power-law fluid contained in a square cavity with the movement of the upper lid and being thermally adiabatic. The other extremities are considered to be at rest, and the base wall is prescribed with uniform/non-uniform temperature distributions. The governing formulation of the problem is handled by executing a finite element approach. Hybrid meshing is performed for domain discretization, and weak variational formulation is utilized for formulation discretization. Second-degree polynomials are employed as the interpolation function, providing information about velocity and temperature distributions at boundary and intermediate nodes. The system of finalized non-linear equations is resolved by using the Paradiso software. The results for velocity and temperature distributions are attained comparatively for uniformly and non-uniformly heated profiles. The kinetic energy and average Nusselt number are also computed against flow concerning variables. From the attained graphical and tabular data, it is deduced that by increasing the Reynolds number, inertial forces dominate over buoyancy forces and the effect of lid movement is prominent on flow characteristics. It is also inferred that for the shear thickening case and for all values of the Reynolds number, the average Nusselt number shows a constant behavior.

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Section: Mathematical Modelingmentioning

confidence: 99%

RETRACTED: Mixed convective heat transfer in a power-law fluid in a square enclosure: Higher order finite element solutions

et al. 2023

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“…The non-singular fractional derivative approach was used in [28] to numerically simulate a mosquito-borne virus. More recent attempts on solutions of fractional order differential equations with various developed methods can be found in the publications [29][30][31][32][33][34][35][36].…”

Section: Introductionmentioning

confidence: 99%

An Efficient Computational Method for Differential Equations of Fractional Type

Türkyılmazoğlu¹

2022

Computer Modeling in Engineering &Amp; Sciences

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An effective solution method of fractional ordinary and partial differential equations is proposed in the present paper. The standard Adomian Decomposition Method (ADM) is modified via introducing a functional term involving both a variable and a parameter. A residual approach is then adopted to identify the optimal value of the embedded parameter within the frame of L 2 norm. Numerical experiments on sample problems of open literature prove that the presented algorithm is quite accurate, more advantageous over the traditional ADM and straightforward to implement for the fractional ordinary and partial differential equations of the recent focus of mathematical models. Better performance of the method is further evidenced against some compared commonly used numerical techniques.

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An approach based on fractional-order Lagrange polynomials for the numerical approximation of fractional order non-linear Volterra-Fredholm integro-differential equations

Kumar

Gupta

2022

J. Appl. Math. Comput.

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Numerical solution of two-dimensional fractional order Volterra integro-differential equations

Cited by 8 publications

References 30 publications

RETRACTED: Mixed convective heat transfer in a power-law fluid in a square enclosure: Higher order finite element solutions

RETRACTED: Mixed convective heat transfer in a power-law fluid in a square enclosure: Higher order finite element solutions

An Efficient Computational Method for Differential Equations of Fractional Type

An approach based on fractional-order Lagrange polynomials for the numerical approximation of fractional order non-linear Volterra-Fredholm integro-differential equations

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