Existence of Positive Solutions for Implicit Caputo Fractional Problems With Integral Boundary Condition

This paper investigates positive solutions for an implicit Caputo fractional boundary value problem of order 0 < ν < 1 on [0, T ] with a nonlocal integral boundary condition. By reformulating the problem as an equivalent nonlinear Volterra integral equation, an associated operator on C ([0, T ], ℝ ) is defined, and fixed‐point theory in a cone is employed. Sufficient conditions are established for the existence of at least one positive solution, and additional criteria are derived for multiple positive solutions. An example is presented to illustrate the applicability of the main results.