Abstract
In this paper, we deal with the newly introduced fractional differential operators, which involve exponential and Mittag-Leffler kernels. First, we find Green’s functions and their properties for conjugate and anti-periodic boundary value problems (BVPs) involving Caputo–Fabrizio (CF) and Atangana–Baleanu–Caputo (ABC) fractional derivatives of order \(1 < \varrho \le 2\). Then, we establish Lyapunov-type inequalities (LTIs) for CF and ABC fractional boundary value problems (FBVPs) using the properties of their Green functions.
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Basua, D., Jonnalagadda, J.M. (2022). Lyapunov-Type Inequalities for Fractional Differential Operators with Non-singular Kernels. In: Giri, D., Raymond Choo, KK., Ponnusamy, S., Meng, W., Akleylek, S., Prasad Maity, S. (eds) Proceedings of the Seventh International Conference on Mathematics and Computing . Advances in Intelligent Systems and Computing, vol 1412. Springer, Singapore. https://doi.org/10.1007/978-981-16-6890-6_58
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DOI: https://doi.org/10.1007/978-981-16-6890-6_58
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