TY - JOUR AU - Alzabut, Jehad AU - Ahmad, Bashir AU - Etemad, Sina AU - Rezapour, Shahram AU - Zada, Akbar PY - 2021 DA - 2021/02/25 TI - Novel existence techniques on the generalized φ-Caputo fractional inclusion boundary problem JO - Advances in Difference Equations SP - 135 VL - 2021 IS - 1 AB - Our basic purpose is to derive several existence aspects of solutions for a novel class of the fractional inclusion problem in terms of the well-defined generalized φ-Caputo and φ-Riemann–Liouville operators. The existing boundary conditions in such an inclusion problem are endowed with mixed generalized φ-Riemann–Liouville conditions. To reach this goal, we utilize the analytical methods on α-ψ-contractive maps and multifunctions involving approximate endpoint specification to derive the required results. In the final part, we formulate an illustrative simulation example to examine obtained theoretical outcomes by computationally and numerically. SN - 1687-1847 UR - https://doi.org/10.1186/s13662-021-03301-3 DO - 10.1186/s13662-021-03301-3 ID - Alzabut2021 ER -