An efficient method for quadratic Riccati differential equation

Aminikhah, Hossein; Hemmatnezhad, M.

doi:10.1016/j.cnsns.2009.05.009

Cited by 68 publications

(45 citation statements)

References 29 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Fractional Riccati equation was solved by many researchers using different methods, such as homotopy analysis method (Cang et al, 2009;Tan and Abbasbandy, 2008), homotopy perturbations method (Abbasbandy, 2006a;Aminikhah and Hemmatnezhad, 2010;Abbasbandy, 2006b), Adomian decomposition (Khan et al, 2011), Gulsu and Sezer (2006) gave a solution of the Riccati equation using the Taylor matrix method and many others.…”

Section: Introductionmentioning

confidence: 99%

“…Fractional calculus has many applications in physics, statistics, engineering and electrochemistry. Many phenomena in these fields modeled using differential equations of fractional order, especially the derivative with respect to the time (Kamke, 1959;Polyanin and Zaitsev, 2003;Soare et al, 2008;Mak and Harko, 2013;Cang et al, 2009;Tan and Abbasbandy, 2008;Abbasbandy, 2006a;Khalil et al, 2014;Aminikhah and Hemmatnezhad, 2010;Khan et al, 2011).…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Analytical Solutions of Riccati Fractional Equation with Coefficients Satisfying Differential Conditions with Arbitrary Function

Jaber¹

2017

Journal of Mathematics and Statistics

View full text Add to dashboard Cite

New exact solutions of the Fractional Riccati Differential equation are presented. Exact solutions are obtained in cases that the coefficient functions and an arbitrary function satisfy some differential conditions. In view of the conditions imposed on Riccati equation's coefficients we define and formulate the coefficients of the Riccati equation to obtain the differential cases, for each case the general solution is presented. The results obtained are useful and confirm the simplicity of the conformable definition of fractional derivative.

show abstract

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Analytical Solutions of Riccati Fractional Equation with Coefficients Satisfying Differential Conditions with Arbitrary Function

Jaber¹

2017

Journal of Mathematics and Statistics

View full text Add to dashboard Cite

show abstract

“…Therefore, science and engineering researchers attempt to propose new methods for solving functional equations. In this paper, we propose a new hybrid of Laplace transform method and new homotopy perturbation method [12] to obtain exact and numerical solutions of the system of two-dimensional Burgers' equation. Finally, three examples are given to illustrate the proposed approach.…”

Section: Introductionmentioning

confidence: 99%

A New Efficient Method for Solving Two-Dimensional Burgers' Equation

Aminikhah

2012

ISRN Computational Mathematics

Self Cite

View full text Add to dashboard Cite

show abstract

“…Therefore, solutions to the Riccati differential equations are important to scientists and engineers. Solving fractional-order Riccati differential equation, the most significant methods are Adomian decomposition method [10], homotopy perturbation method [11][12][13][14], homotopy analysis method [15,16], Taylor matrix method [17], Haar wavelet method [18], and combination of Laplace, Adomian decomposition, and Padé approximation [19] methods.…”

Section: Introductionmentioning

confidence: 99%

Legendre Wavelet Operational Matrix Method for Solution of Riccati Differential Equation

Balaji

2014

International Journal of Mathematics and Mathematical Sciences

View full text Add to dashboard Cite

A Legendre wavelet operational matrix method (LWM) is presented for the solution of nonlinear fractional-order Riccati differential equations, having variety of applications in quantum chemistry and quantum mechanics. The fractional-order Riccati differential equations converted into a system of algebraic equations using Legendre wavelet operational matrix. Solutions given by the proposed scheme are more accurate and reliable and they are compared with recently developed numerical, analytical, and stochastic approaches. Comparison shows that the proposed LWM approach has a greater performance and less computational effort for getting accurate solutions. Further existence and uniqueness of the proposed problem are given and moreover the condition of convergence is verified.

show abstract

An efficient method for quadratic Riccati differential equation

Cited by 68 publications

References 29 publications

Analytical Solutions of Riccati Fractional Equation with Coefficients Satisfying Differential Conditions with Arbitrary Function

Analytical Solutions of Riccati Fractional Equation with Coefficients Satisfying Differential Conditions with Arbitrary Function

A New Efficient Method for Solving Two-Dimensional Burgers' Equation

Legendre Wavelet Operational Matrix Method for Solution of Riccati Differential Equation

Contact Info

Product

Resources

About