4 SOLVING ABEL INTEGRAL EQUATIONS OF FIRST KIND VIA FRACTIONAL CALCULUS
S. JahanshahiDepartment of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, IranE. BabolianDepartment of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, IranD. F. M. TorresCenter for Research and Development in Mathematics and Applications (CIDMA), Department of Mathematics, University of Aveiro, 3810-193 Aveiro, PortugalA. R. VahidiDepartment of Mathematics, Shahre Rey Branch, Islamic Azad University, Tehran, Iran
2016en
ABI
Annotatsiya
We give a new method for numerically solving Abel integral equations of first kind. An estimation for the error is obtained. The method is based on approximations of fractional integrals and Caputo derivatives. Using trapezoidal rule and Computer Algebra System Maple, the exact and approximation values of three Abel integral equations are found, illustrating the effectiveness of the proposed approach.
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