Approximate numerical solutions of fractional integral equations using Laguerre and Touchard polynomials
Supriya Kumar Paul, Lakshmi Narayan Mishra∗ and Vishnu Narayan Mishra
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Two numerical methods based on Laguerre and Touchard polynomials are de scribed in this paper to solve both the fractional integral equations of the first kind and the second kind (FIEs-1K and FIEs-2K, respectively). The fractional integrals are described in the Erd´ elyi-Kober sense. Both the integral equations are transformed into an algebraic system of linear equations using the Laguerre and Touchard matrices. All the steps of the algorithm are given to find the solutions. Also, the accuracy of the solutions has been demonstrated. Five examples are provided to interpret the methods. The accuracy of solutions is compared for both methods. MATLAB program is used to perform all computations and graphs.