Bernstein Collocation Method for the Solution of Fractional Integro-differential Equations

Oyedepo T., Ishola C. Y., Aminu T. F., Akpan C. E.

Abstract


The main purpose of this study is to present an approximation method based on the Bernstein polynomials for fractional integro-differential equations. This method transforms the integro-differential equation to a system of linear algebraic equations by using the collocation points, which is then solved using MAPLE 18. Besides, some examples are presented to illustrate the accuracy of the method and the results were presented in graphical form.


Full Text:

PDF

References


Adam, L. (2004): Fractional Calculus: history, definition and application for the engineer. Dept of Aerospace and Mechanical Engineering University of Notre Dame.

Caputo, M. (1967): Linear models of dissipation whose Q is almost frequency Independent. Geophysical Journal International, 13(5):529 – 539.

Khowsrow M., Monireh N.S & Azadeh O. (2013). Numerical solution of fractional integro- Differential equation by using cubic B-spline wavelets. Proceeding of the world Congress on Engineering U .K, 1, 3-5

Mittal, R. C. and Nigam, R. (2008): Solution of Fractional Integro-differential Equations by Adomian Decomposition Method. International Journal of Applied Mathematics and Mechanics, 4(2), 87-94.

Munkhammar, J. D. (2005): Fractional calculus and the Taylor Riemann series. Undergraduate Mathematics Journal, 5(1): 1 - 19.

Mohamed, S, Muteb R. and Refah A. (2016). Solving fractional integro-differential equations by homotopy analysis transform method. International Journal of pure and Applied Mathematics, 106(4), 1037 - 1055

Mohammed, D.Sh. (2014): Numerical solution of fractional integro-differential equations by least square method and shifted chebyshev polynomial. MathematicsDepartment, Faculty of science, Zagazig University, Zagazig, Egypt.

Momani, S. and Qaralleh A. (2006): An efficient method for solving systems of Fractional Integro-differential equations. Computer and Mathematica with Applications vol.25, 459-570.

Oyedepo, T., Taiwo, O.A., Abubakar J. U., & Ogunwobi, Z.O. (2016): Numerical Studies for Solving Fractional Integro-Differential Equations by using Least Squares Method and Bernstein Polynomials. Fluid Mechanics Open Access 3(3): 1-7

Podlubny, I. (1999): Fractional differential equations: an introduction to fractional

Derivatives, fractional differential equations, to methods of their solution and some of their applications. New York: Academic Press. 19

Samko, S.G., Kilbas, A.A. and Marichev O.I (1993): Fractional Integrals and Derivatives. Theory and Applications, Gordon and Breach, Yverdon.

Rawashdeh, E.A (2006): Numerical solution of fractional integro-differential equations by collocation method. Appl Math Comput. 176 .1-6

TTaiwo, O. A. & Fesojaye M. O. (2015). Perturbation Least-Squares Chebyshev method for solving fractional order integro-differential equations. Theoretical Mathematics and Applications, 5(4), 37 – 47


Refbacks

  • There are currently no refbacks.