On the Solutions Fractional Riccati Differential Equation with Modified Riemann-Liouville Derivative

Merdan, Mehmet

doi:10.1155/2012/346089

Cited by 34 publications

(31 citation statements)

References 23 publications

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“…(13), from the point of view total absolute errors in t = 0.1, 0.2, · · · , 0.9, is CW method. Therefore, for summarizing the discussion, we give in Table 1, only comparison of our method with CW method (for µ = 192) and fractional variational iteration method (FVIM) presented in [15] for α = 0.5, 1. Table 2, shows the sum of the absolute errors in points t = 0.1, 0.2, · · · , 0.9, for all methods listed in this problem with α = 1.…”

Section: Numerical Discussion Of the Fractional Riccati Differential mentioning

confidence: 99%

Hybrid functions approach for the fractional Riccati differential equation

Maleknejad

Torkzadeh

2016

Filomat

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In this paper, we state an efficient method for solving the fractional Riccati differential equation.This equation plays an important role in modeling the various phenomena in physics and engineering. Our approach is based on operational matrices of fractional differential equations with hybrid of block-pulse functions and Chebyshev polynomials. Convergence of hybrid functions and error bound of approximation by this basis are discussed. Implementation of this method is without ambiguity with better accuracy than its counterpart other approaches. The reliability and efficiency of the proposed scheme are demonstrated by some numerical experiments.

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Section: Numerical Discussion Of the Fractional Riccati Differential mentioning

confidence: 99%

Hybrid functions approach for the fractional Riccati differential equation

Maleknejad

Torkzadeh

2016

Filomat

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“…Remark 4. Example 3 has been solved using HAM [24], ADM [25], VIM [26], and HPM [27,28], and recently it was solved in [29]. Comparison of the results of applying the HDM with others methods leads to significant consequences.…”

Section: Applicationmentioning

confidence: 99%

Solving Partial Differential Equation with Space- and Time-Fractional Derivatives via Homotopy Decomposition Method

Atangana

Belhaouari

2013

Mathematical Problems in Engineering

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The analytical solution of the partial differential equation with time-and space-fractional derivatives was derived by means of the homotopy decomposition method (HDM). Some examples are given and comparisons are made. The evaluations show that the homotopy decomposition method is extremely successful and suitable. The achieved results make the steadfastness of the HDM and its wider applicability to fractional differential equation obvious. Additionally, the adding up implicated in HDM is exceptionally undemanding and uncomplicated. It is confirmed that HDM is an influential and professional apparatus for FPDEs. It was also established that HDM is supplementary well organized than the ADM, VIM, HAM, and HPM.

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“…They were used as a tool for rapid global search method and simulated annealing for efficient local search method. A fractional variational iteration method described in the Riemann-Liouville derivative has been applied in [21], to give an analytical approximate solution to nonlinear fractional Riccati differential equation. A combination of finite 2 International Journal of Mathematics and Mathematical Sciences difference method and Padé-variational iteration numerical scheme was proposed by Sweilam et al [22].…”

Section: Introductionmentioning

confidence: 99%

Legendre Wavelet Operational Matrix Method for Solution of Riccati Differential Equation

Balaji

2014

International Journal of Mathematics and Mathematical Sciences

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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.

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On the Solutions Fractional Riccati Differential Equation with Modified Riemann-Liouville Derivative

Cited by 34 publications

References 23 publications

Hybrid functions approach for the fractional Riccati differential equation

Hybrid functions approach for the fractional Riccati differential equation

Solving Partial Differential Equation with Space- and Time-Fractional Derivatives via Homotopy Decomposition Method

Legendre Wavelet Operational Matrix Method for Solution of Riccati Differential Equation

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