Mathematical Model In Existence and Uniqueness In Nonlinear Order

This paper is devoted to proving the existence, uniqueness and smoothness of solutions for differential equations with Riemann-Liouville sequential fractional derivatives admitting only the existence of a lower solution. The appropriate fractional Sobolev spaces equipped with a suitable partial order are introduced, and applying some fixed point theorems the results are proved. The approximate solutions are presented to the corresponding initial value problems. A few illustrative examples are given.