Solution of fractional integro-differential equations by using fractional differential transform method. (English) Zbl 1197.45001

Summary: The fractional differential transform method (FDTM), which is a semi analytical numerical technique, is extended to solve fractional integro-differential equations of Volterra type. New theorems for the transformation of integral terms having degenerate kernels that never existed before are introduced with their proofs. This implemented new technique is validated by solving and comparing four different examples that exist in the literature. It is observed that, FDTM can be utilized as a powerful and reliable tool for the solution of fractional integro-differential equations.
Editorial remark: There are doubts about a proper peer-reviewing procedure of this journal. The editor-in-chief has retired, but, according to a statement of the publisher, articles accepted under his guidance are published without additional control.


45A05 Linear integral equations
34A08 Fractional ordinary differential equations
26A33 Fractional derivatives and integrals
45D05 Volterra integral equations
Full Text: DOI


[1] Munkhammar, J. D., Fractional calculus and the Taylor-Riemann series, Undergrad J Math, 6 (2005)
[2] Podlubny, I., Fractional differential equations: an introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications (1999), Academic Press: Academic Press New York · Zbl 0924.34008
[3] Caputo, M., Linear models of dissipation whose Q is almost frequency independent. Part II, J Roy Austral Soc, 13, 529-539 (1967)
[4] Momani, S.; Noor, M. A., Numerical methods for fourth order fractional integro-differential equations, Appl Math Comput, 182, 754-760 (2006) · Zbl 1107.65120
[5] Momani, S.; Qaralleh, A., An efficient method for solving systems of fractional integro-differential equations, Comput Math Appl, 52, 459-470 (2006) · Zbl 1137.65072
[6] Rawashdeh, E. A., Numerical solution of fractional integro-differential equations by collocation method, Appl Math Comput, 176, 1-6 (2006) · Zbl 1100.65126
[7] Arikoglu, A.; Ozkol, I., Solution of fractional differential equations by using differential transform method, Chaos, Solitons, & Fractals, 34, 1473-1481 (2007) · Zbl 1152.34306
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.