Abstract
AbstractIn 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.KeywordsFractional derivativeBoundary value problemLyapunov-type inequalityExponentialMittag-Leffler
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