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A constant enclosure method for validating existence and uniqueness of the solution of an initial value problem for a fractional differential equation |
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| Authors: | M Amairi M Aoun MN Abdelkrim |
| Institution: | Research Unit Modeling, Analysis and Control of Systems (MACS), National Engineering School of Gabès (ENIG), Gabès, Tunisia |
| Abstract: | This paper presents a new method for validating existence and uniqueness of the solution of an initial value problems for fractional differential equations. An algorithm selecting a stepsize and computing a priori constant enclosure of the solution is proposed. Several illustrative examples, with linear and nonlinear fractional differential equations, are given to demonstrate the effectiveness of the method. |
| Keywords: | Fractional order differential equations Caputo fractional derivative Initial value problems Existence and uniqueness Interval analysis Validated computing |
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