This article proposes a simple method to obtain approximate numerical solution of a singular fractional order integro-differential equation with Cauchy kernel by using Bernstein polynomials as basis. The fractional derivative is described in Caputo sense. The properties of Bernstein polynomials are used to reduce the fractional order integro-differential equation to the solution of algebraic equations. The numerical results obtained by the present method compares favorably with those obtained earlier for the first order integro-differential equation. Also the convergence of the method is established rigorously.
Chatterjee, Avipsita; Basu, Uma; and Mandal, B. N.
Solution of a Cauchy singular fractional integro-differential equation in Bernstein polynomial basis,
Applications and Applied Mathematics: An International Journal (AAM), Vol. 11,
2, Article 18.
Available at: https://digitalcommons.pvamu.edu/aam/vol11/iss2/18