Fractional calculus and applications
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Organizer(s): |
Name:
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Affiliation:
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Country:
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Abdon Atangana
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University of the Free State
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So Africa
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Abstract:
| | The concept of differentiation and integration was initiated by Leibniz and applied in classical mechanic. Modellers rely on these concept to predict and control the environment they live in. A good prediction can only be achieved in three steps, the first is to observe the given physical problem, second to convert the observed facts into a mathematical formation, and the last step is to provide exact solution for simple case and numerical solution for complex cases. While the concept was used with great success for some classical problems, while the concept has been used to model some simple real world problems, it was revealed in many already published research that this concept cannot really handle processes following non-Markovian principle, that is to say they cannot predict some complex problems requiring inclusion of memory effect. To solve this problem, mankind suggested a new differential and integral operator based on convolution. This type is known as fractional differential and integral operators; in particular the fractional derivative is convolution of the classical derivative with kernel. Three kernels have been suggested, the power law, exponential and finally the generalized Mittag-Leffler function. |
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