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Fractional-order Bessel functions with various applications. (English) Zbl 07144731
Summary: We introduce fractional-order Bessel functions (FBFs) to obtain an approximate solution for various kinds of differential equations. Our main aim is to consider the new functions based on Bessel polynomials to the fractional calculus. To calculate derivatives and integrals, we use Caputo fractional derivatives and Riemann-Liouville fractional integral definitions. Then, operational matrices of fractional-order derivatives and integration for FBFs are derived. Also, we discuss an error estimate between the computed approximations and the exact solution and apply it in some examples. Applications are given to three model problems to demonstrate the effectiveness of the proposed method.

##### MSC:
 34A08 Fractional ordinary differential equations 65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs 65L70 Error bounds for numerical methods for ordinary differential equations
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