| Abstract: |
| We prove existence of three positive solutions for a class of Caputo fractional differential equation with nonlocal boundary conditions involving both the first and second-order derivatives. Our result extends the Riemann-Liouville fractional system to the Caputo equation. By converting the problem into a Caputo integral operator, we employ the Leggett-Williams fixed point theorem to establish conditions that ensure existence of three positive solutions. We illustrate the result with examples and numerical simulations that demonstrate one or more nontrivial solutions and highlight parameter regimes yielding multiplicity. |
|