TY - JOUR AU - Thabet, Sabri T. M. AU - Etemad, Sina AU - Rezapour, Shahram PY - 2020 DA - 2020/11/11 TI - On a new structure of the pantograph inclusion problem in the Caputo conformable setting JO - Boundary Value Problems SP - 171 VL - 2020 IS - 1 AB - In this work, we reformulate and investigate the well-known pantograph differential equation by applying newly-defined conformable operators in both Caputo and Riemann–Liouville settings simultaneously for the first time. In fact, we derive the required existence criteria of solutions corresponding to the inclusion version of the three-point Caputo conformable pantograph BVP subject to Riemann–Liouville conformable integral conditions. To achieve this aim, we establish our main results in some cases including the lower semi-continuous, the upper semi-continuous and the Lipschitz set-valued maps. Eventually, the last part of the present research is devoted to proposing two numerical simulative examples to confirm the consistency of our findings. SN - 1687-2770 UR - https://doi.org/10.1186/s13661-020-01468-4 DO - 10.1186/s13661-020-01468-4 ID - Thabet2020 ER -