• SOLUTION OF ABEL’S INTEGRAL EQUATIONS USING LEGENDRE POLYNOMIALS AND FRACTIONAL CALCULUS TECHNIQUES

Z. Avazzadeh*, B. Shafiee, G. B. Loghmani

Abstract


In this paper, we offer a new approach for solving Abel’s integral equations as singular integral equation. Since Abel’s integral equation can be considered the fractional integral equation, we use fractional integral for solving it. The fractional operator is considered in the sense of Riemann- Liouville. Computation of fractional integral for arbitrary function are directly hard and cost, hence we approximate the integrand function by Legendre polynomials. Although Abel’s integral equations as convolution and singular integral equation are heavily and difficult in computation, some numerical examples shows high accurate and good efficiency.

Keywords


Abel’s integral equation; Fractional calculus; Legendre polynomial; Collocation method.

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