Existence and uniqueness for a fractional differentialequation involving Atangana-Baleanu derivative byusing a new contraction

In this study, by using some new contractions, we obtain an existence and uniqueness conclusion for afractional differential equation with Atangana-Baleanu derivative as follows:(ABC0Dκδ)(s) =h(s,δ(s)),s∈J,0≤κ≤1,(1)δ(0) =δ0,whereDςis the Atangana-Baleanu derivative of orderςandfis continuous withf(0,}(0)) = 0.

Related Organizations

University of Bonab
Iran (Islamic Republic of)
Azarbaijan Shahid Madani University
Iran (Islamic Republic of)

Keywords

Atangana-Baleanu fractional derivative, orbitally complete, fixed point.

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