Generalized Differential Transform Method – Application to Integral Equations of Fractional Order
DOI:
https://doi.org/10.18311/jmmf/2023/34153Keywords:
Abel Integral Equation, Differential Transform Method, Generalized Differential Transform Method, Caputo Sense.Abstract
In this paper, we have used gener-alized differential transform method to solve different types of integral equations of fractional order. All the fractional integrals are written in the Riemann-Liouville sense and fractional derivatives are written in the Caputo sense.
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References
S.A. Yousefi, (2006): Numerical solution of Abels integral equation by using Legendre wavelets, Appl. Math. Comp. 175 (2006) 574-580. DOI: https://doi.org/10.1016/j.amc.2005.07.032
Y. Liu, L. Tao, (2007): Mechanical quadrature methods and their extrapolation for solving first kind Abel integral equations, Jour. Comput. Appl. Math. 201 (2007) 300-313 . DOI: https://doi.org/10.1016/j.cam.2006.02.021
S. Dixit, R. K. Pandey, S. Kumar, O.P. Singh, (2011): Solution of the Generalized Abel Integral Equation by using Almost Bernstein Operational Matrix, American Jour. Comput. Math.1 (2011) 226-234. DOI: https://doi.org/10.4236/ajcm.2011.14026
R. K. Pandey, S. Sharma, K. Kumar, (2016): Collocation method for Generalized Abel’s Integral Equations, Jour. Comput. Appl. Math. 302 (2016) 118-128. DOI: https://doi.org/10.1016/j.cam.2016.01.036
M. Caputo, (1967): Linear models of dissipation whose Q is almost frequency independent, Part II. J Roy Austral Soc 13 (1967) 529-539. DOI: https://doi.org/10.1111/j.1365-246X.1967.tb02303.x
Z. Odibat, S.Momani, V.S. Erturk, (2008): Generalized differential transform method: Application to differential equations of fractional order, Appl. Math. Comput. 197 (2008) 467-477. DOI: https://doi.org/10.1016/j.amc.2007.07.068