Solution of Abel Integral Equation Using Differential Transform Method

Subhabrata Mondal; B. N. Mandal

doi:10.24297/jam.v14i1.7172

Authors

Subhabrata Mondal University of Calcutta
B. N. Mandal Indian Statistical Institute

DOI:

https://doi.org/10.24297/jam.v14i1.7172

Keywords:

Abel Integral Equation, Differential Transform Method, Fractional Differential Transform Method

Abstract

The application of fractional differential transform method, developed for differential equations of fractional order, are extended to derive exact analytical solutions of fractional order Abel integral equations. The fractional integrations are described in the Riemann-Liouville sense and fractional derivatives are described in the Caputo sense. Abel integral equation occurs in the mathematical modeling of various problems in physics, astrophysics, solid mechanics and applied sciences. An analytic technique for solving Abel integral equation of first kind by the proposed method is introduced here. Also illustrative examples with exact solutions are considered to show the validity and applicability of the proposed method. Abel integral equation, Differential transform method, Fractional differential transform method.

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Author Biographies

Subhabrata Mondal, University of Calcutta

Department of Applied Mathematics, University of Calcutta, 92, A.P.C. Road, Kolkata-700009, India.

B. N. Mandal, Indian Statistical Institute

Physics and Applied Mathematics Unit, Indian Statistical Institute, 203, B.T Road, Kolkata-700108, India

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