Approximate solution of nonlinear quadratic integral equations of fractional order via piecewise linear functions. (English) Zbl 1377.65171
Summary: In this paper, the main objective is to describe an approximate scheme for solving nonlinear quadratic integral equations (NQIEs) of fractional order. The method is based on piecewise linear functions that are called hat functions (HFs). By applying the HFs approximation, their properties and operational matrices, nonlinear equation becomes to a nonlinear system of equations which can be solved by using simple arithmetic methods. Also, the error analysis of HFs method and convergence analysis of proposed model are given. At the end, two nonlinear examples are presented to illustrate the validity and applicability of the explained approach.
MSC:
| 65R20 | Numerical methods for integral equations |
| 45G10 | Other nonlinear integral equations |
| 26A33 | Fractional derivatives and integrals |
Keywords:
hat functions; nonlinear quadratic integral equation; fractional calculus; operational matrix; error analysis; numerical example; convergenceReferences:
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