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Maleknejad, K., Nouri, K., Torkzadeh, L. (2017). Study on multi-order fractional differential equations via operational matrix of hybrid basis functions. Bulletin of the Iranian Mathematical Society, 43(2), 307-318.
K. Maleknejad; K. Nouri; L. Torkzadeh. "Study on multi-order fractional differential equations via operational matrix of hybrid basis functions". Bulletin of the Iranian Mathematical Society, 43, 2, 2017, 307-318.
Maleknejad, K., Nouri, K., Torkzadeh, L. (2017). 'Study on multi-order fractional differential equations via operational matrix of hybrid basis functions', Bulletin of the Iranian Mathematical Society, 43(2), pp. 307-318.
Maleknejad, K., Nouri, K., Torkzadeh, L. Study on multi-order fractional differential equations via operational matrix of hybrid basis functions. Bulletin of the Iranian Mathematical Society, 2017; 43(2): 307-318.

Study on multi-order fractional differential equations via operational matrix of hybrid basis functions

Article 5, Volume 43, Issue 2, April 2017, Page 307-318  XML PDF (152 K)
Document Type: Research Paper
Authors
K. Maleknejad 1; K. Nouri2; L. Torkzadeh2
1School of‎ ‎Mathematics‎, ‎Iran University of Science & Technology‎, ‎Narmak‎, ‎Tehran 16846 13114‎, ‎Iran.
2Department of Mathematics‎, ‎Faculty of Mathematics‎, ‎Statistics‎ ‎and Computer Sciences‎, ‎Semnan University‎, ‎P.O‎. ‎Box 35195-363‎, ‎Semnan‎, ‎Iran.
Receive Date: 28 February 2014,  Revise Date: 24 September 2015,  Accept Date: 14 November 2015 
Abstract
In this paper we apply hybrid functions of general block-pulse‎ ‎functions and Legendre polynomials for solving linear and‎ ‎nonlinear multi-order fractional differential equations (FDEs)‎. ‎Our approach is based on incorporating operational matrices of‎ ‎FDEs with hybrid functions that reduces the FDEs problems to‎ ‎the solution of algebraic systems‎. ‎Error estimate that verifies a‎ ‎convergence of the approximate solutions is considered‎. ‎The‎ ‎numerical results obtained by this scheme have been compared with‎ ‎the exact solution to show the efficiency of the method‎.
Keywords
Fractional derivatives and integrals‎; ‎multi-order fractional differential equations‎; ‎operational matrix‎; ‎hybrid functions‎
Main Subjects
40-XX Sequences, series, summability
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