Positive solutions to fractional boundary-value problems with p-Laplacian on time scales

In this article, we consider the following boundary-value problem of nonlinear fractional differential equation with p-Laplacian operator: $${aligned}& Dα(φₚ(Dαu(t)))= f (t, u(t)), t∈ [0,1]T, \& u(0)= u(σ (1))= Dαu(0)= Dαu(σ (1))=0, {aligned}$$ where $1<α ≤ 2$ is a real number, the time scale T is a nonempty closed subset of $R$ . $Dα$ is the conformable fractional derivative on time scales, $φₚ(s)= s ᵖ⁻²s$ , $p>1$ , $φₚ⁻¹=φq$ , $1/p+1/q=1$ , and $f:[0, σ (1)]× [0,+ ∞ )→ [0,+∞ )$ is continuous. By the use of the approach method and fixed-point theorems on cone, some existence and multiplicity results of positive solutions are acquired. Some examples are presented to illustrate the main results.