A complex valued approach to the solutions of Riemann-Liouville integral, Atangana-Baleanu integral operator and non-linear Telegraph equation via fixed point method

This paper involves complex valued versions of Riemann-Liouville integral, Atangana-Baleanu integral operator and non-linear Telegraph equation. Under various suitable assumptions the results are established in the setting of complex valued double controlled metric space. Thereafter, by making consequent use of the fixed point method, short and simple proofs are obtained for solutions of Riemann-Liouville integral, complex valued Atangana-Baleanu integral operator and non-linear Telegraph equation. (C) 2019 Elsevier Ltd. All rights reserved.