A higher-order extension of Atangana–Baleanu fractional operators with respect to another function and a Gronwall-type inequality

Abstract This paper aims to extend the Caputo–Atangana–Baleanu ( A B C $ABC$ ) and Riemann–Atangana–Baleanu ( A B R $ABR$ ) fractional derivatives with respect to another function, from fractional order μ ∈ ( 0 , 1 ] $\mu \in (0,1]$ to an arbitrary order μ ∈ ( n , n + 1 ] $\mu \in (n,n+1]$ , n = 0 ,...

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