Abstract
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 phi -Caputo and phi -Riemann-Liouville operators. The existing boundary conditions in such an inclusion problem are endowed with mixed generalized phi -Riemann-Liouville conditions. To reach this goal, we utilize the analytical methods on alpha-psi -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.