Abstract
Fractional differentiation and integration have witness a continuous revolution in the last decades as they have been found to capture behaviors that resemble properties of some mathematical functions for example power law, exponential decay and crossover from exponential decay to power law. We have presented different differential operators with power law, exponential decay and the generalized Mittag-Leffler kernels. Using the fundamental theorem of calculus, integral operators associated to these differential operators were presented. Different properties of these nonlocal operators have been presented in details. Using some approximation techniques, both fractional differential and integral operators were discretized.
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© 2022 The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.
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Atangana, A., İgret Araz, S. (2022). Fractional Differential and Integral Operators. In: Fractional Stochastic Differential Equations. Industrial and Applied Mathematics. Springer, Singapore. https://doi.org/10.1007/978-981-19-0729-6_2
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DOI: https://doi.org/10.1007/978-981-19-0729-6_2
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Publisher Name: Springer, Singapore
Print ISBN: 978-981-19-0728-9
Online ISBN: 978-981-19-0729-6
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