Approximations of the Fractional Integral and Numerical Solutions of Fractional Integral Equations

doi:10.1007/s42967-021-00132-7

Communications on Applied Mathematics and Computation ›› 2021, Vol. 3 ›› Issue (3): 545-569.doi: 10.1007/s42967-021-00132-7

Approximations of the Fractional Integral and Numerical Solutions of Fractional Integral Equations

Yuri Dimitrov^1,2

1 Department of Mathematics and Physics, University of Forestry, 1756 Sofia, Bulgaria;
2 Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, 1113 Sofia, Bulgaria

Received:2020-08-24 Revised:2020-11-18 Online:2021-09-20 Published:2021-09-16
Contact: Yuri Dimitrov E-mail:yuri.dimitrov@ltu.bg
Supported by:
This work was supported by the Bulgarian National Science Fund under Project KP-06-M32/2 "Advanced Stochastic and Deterministic Approaches for Large-Scale Problems of Computational Mathematics"

Abstract

Abstract: In the present paper, we derive the asymptotic expansion formula for the trapezoidal approximation of the fractional integral. We use the expansion formula to obtain approximations for the fractional integral of orders α, 1 + α, 2 + α, 3 + α and 4 + α. The approximations are applied for computation of the numerical solutions of the ordinary fractional relaxation and the fractional oscillation equations expressed as fractional integral equations.

Key words: Fractional integral, Trapezoidal approximation, Fractional integral equation, Finite-difference scheme

CLC Number:

Yuri Dimitrov. Approximations of the Fractional Integral and Numerical Solutions of Fractional Integral Equations[J]. Communications on Applied Mathematics and Computation, 2021, 3(3): 545-569.

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Approximations of the Fractional Integral and Numerical Solutions of Fractional Integral Equations

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