1
PhD Candidate, Faculty of Mathematical Sciences, Shahrekord University
2
Associate Professor, Faculty of Mathematical Sciences, Shahrekord University
Abstract
In this paper, we introduce a system of fractional differential equations in the sense of the Prabhakar fractional derivative and by applying the Laplace transform we get the solution of the system with respect to the Mittag-Leffler function with three parameters. For obtaining the existence and uniqueness of the solution, we construct the sequence of iterates for the solution and by using the Picard-Lindelof theorem, we prove the existence and uniqueness of the solution of the system. Finally, we give an example by using the stated theorem.
Derakhshan, M. H., Ansari, A., & Ahanjideh, N. (2017). Picard-Lindelof method for initial value problems with Prabhakar fractional derivative. سیستم های مختلط و غیر خطی, 1(1), 55-62.
MLA
Mohammad Hossein Derakhshan; Alireza Ansari; Neda Ahanjideh. "Picard-Lindelof method for initial value problems with Prabhakar fractional derivative". سیستم های مختلط و غیر خطی, 1, 1, 2017, 55-62.
HARVARD
Derakhshan, M. H., Ansari, A., Ahanjideh, N. (2017). 'Picard-Lindelof method for initial value problems with Prabhakar fractional derivative', سیستم های مختلط و غیر خطی, 1(1), pp. 55-62.
VANCOUVER
Derakhshan, M. H., Ansari, A., Ahanjideh, N. Picard-Lindelof method for initial value problems with Prabhakar fractional derivative. سیستم های مختلط و غیر خطی, 2017; 1(1): 55-62.
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