An efficient hybrid numerical method for multi-term time fractional partial differential equations in fluid mechanics with convergence and error analysis

Joujehi, A. Soltani; Derakhshan, Mohammadhossein; Marasi, Hamidreza

doi:10.1016/j.cnsns.2022.106620

Cited by 13 publications

(4 citation statements)

References 43 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The exact solution of this example for S = 2 is given by u(x, t) = t 3 2 x 2 (1 − x) 4 . We use the proposed method with 𝜚 1 = 1.25, 𝜚 2 = 1.5 for different values of M to estimate the solution u(s, t) by various values of mesh points.…”

Section: Experimental Simulationsmentioning

confidence: 99%

“…The theory of fractional-order calculus has gained a lot of practical applications in recent years, and it has been used to model many interesting phenomena including chaos theory, bio-mathematics, financial models, and optics [1][2][3][4]. The analytical and numerical solutions for fractional-order differential equations that appeared in various models play a vital role in illustrating the characteristics of nonlinear complex problems in our daily life.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Numerical solution of multidimensional time‐space fractional differential equations of distributed order with Riesz derivative

Mohammed Ghuraibawi,

Marasi,

Derakhshan

et al. 2023

Math Methods in App Sciences

Self Cite

View full text Add to dashboard Cite

In this article, we derive a computational scheme joining the finite difference and operational matrix methods to numerically simulate fractional differential equations of distributed order with Riesz derivatives subject to the initial and Dirichlet boundary conditions. The finite difference method is used to discretize Riesz‐space fractional derivatives, and the operational matrix method is based on fractional shifted Gegenbauer functions for the approximation of time derivatives. The derived method transforms the given equation into a system of linear algebraic equations. For the numerical solution, we derive the optimal error bound and prove the theoretical unconditional stability with respect to the ‐norm. Furthermore, we numerically verify the stability of the proposed method. We observe the accuracy of the second order of the given schemes. The accuracy and effectiveness of the method are checked to solve some problems of telegraph equations. The CPU running time for the method with a fractional shifted Gegenbauer basis is much less than for methods with other bases.

show abstract

Section: Experimental Simulationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Numerical solution of multidimensional time‐space fractional differential equations of distributed order with Riesz derivative

Mohammed Ghuraibawi,

Marasi,

Derakhshan

et al. 2023

Math Methods in App Sciences

Self Cite

View full text Add to dashboard Cite

show abstract

“…Exact solution of linear multi-term fractional diffusion equations with q i being positive constants on bounded domains are constructed employing eigenfunction expansion in [6,7,14,34,45]. We quote [34,41,42,45] where certain numerical solutions are built to the corresponding initialboundary value problems to evolution equations with D t given via (1.6). Abstract multi-term timefractional equations in Banach spaces are discussed in [27].…”

Section: Introductionmentioning

confidence: 99%

Initial-boundary value problems to semilinear multi-term fractional differential equations

Siryk¹,

Vasylyeva²

2023

Preprint

View full text Add to dashboard Cite

For ν, ν i , µ j ∈ (0, 1), we analyze the semilinear integro-differential equation on the onedimensional domain Ω = (a, b) in the unknown u = u(x, t)where, L k are uniform elliptic operators with time-dependent smooth coefficients, K is a summable convolution kernel. Particular cases of this equation are the recently proposed advanced models of oxygen transport through capillaries. Under certain structural conditions on the nonlinearity f and orders ν, ν i , µ j , the global existence and uniqueness of classical and strong solutions to the related initial-boundary value problems are established via the so-called continuation arguments method. The crucial point is searching suitable a priori estimates of the solution in the fractional Hölder and Sobolev spaces. The problems are also studied from the numerical point of view.

show abstract

“…Nowadays, differential equations of fractional order as extension of the differential equations of integer order play a fundamental role in the modeling of many scientific, practical, and important problems [1][2][3][4][5][6][7][8][9][10]. Recently, several numerical methods have been proposed to simulate various types of fractional-order systems [11][12][13].…”

Section: Introductionmentioning

confidence: 99%

An efficient numerical method for the time-fractional distributed order nonlinear Klein–Gordon equation with shifted fractional Gegenbauer multi-wavelets method

et al. 2023

View full text Add to dashboard Cite

In this paper, we propose an effective numerical method, based on the use of two-dimensional Shifted fractional-order Gegenbauer Multi-wavelets, for finding the approximate solutions of the time-fractional distributed order non-linear partial differential equations. The method is applied to solve fractional distributed order non-linear Klein-Gordon equation, numerically. We derive an exact formula for the Riemann–Liouville fractionalintegral operator for the Shifted fractional Gegenbauer Multi-wavelets.Applying function approximations obtained by this method turns the considered equation into a system of algebraic equations. Error estimation and convergence analysis of the methodare also studied. Some numerical examples are included to show and check the effectiveness of the proposed method.

show abstract

An efficient hybrid numerical method for multi-term time fractional partial differential equations in fluid mechanics with convergence and error analysis

Cited by 13 publications

References 43 publications

Numerical solution of multidimensional time‐space fractional differential equations of distributed order with Riesz derivative

Numerical solution of multidimensional time‐space fractional differential equations of distributed order with Riesz derivative

Initial-boundary value problems to semilinear multi-term fractional differential equations

An efficient numerical method for the time-fractional distributed order nonlinear Klein–Gordon equation with shifted fractional Gegenbauer multi-wavelets method

Contact Info

Product

Resources

About