<p>Numerical treatment of fractional terminal value problems presents significant challenges, particularly when solutions exhibit low regularity near the final time. Such behavior often arises from weak singularities introduced by right-sided fractional derivatives. Traditional spectral collocation methods often lose convergence under these conditions, and existing smoothing transformation techniques, while successful for rational fractional orders, struggle when the order is irrational. In this work, we propose a novel spectral collocation approach for nonlinear fractional differential equations with right-sided Caputo derivatives, using second-kind fractional Legendre polynomials as basis functions. These polynomials are uniquely suited to capture terminal singularities and handle low-regularity, nonlocal solutions, without being limited to rational fractional orders. To the best of our knowledge, this is the first time second-kind fractional Legendre polynomials are applied to right-sided fractional problems. Furthermore, we study the existence and uniqueness of the numerical solution of the proposed collocation scheme. Through rigorous <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(L^2_{\chi ^{0,0,\mu }}\)</EquationSource> <EquationSource Format="MATHML"><math> <msubsup> <mi>L</mi> <msup> <mi>χ</mi> <mrow> <mn>0</mn> <mo>,</mo> <mn>0</mn> <mo>,</mo> <mi>μ</mi> </mrow> </msup> <mn>2</mn> </msubsup> </math></EquationSource> </InlineEquation> analysis and comprehensive numerical experiments, we demonstrate that the proposed method attains high-order accuracy, even for solutions with irrational fractional orders and nonsmooth behavior, highlighting its robustness and broad applicability.</p>