The　fractional　model　which　played　an　essential　role　in　nuclear　and　particle　physics　used　to　describe　the　nuclear　element　interaction　is　the　Phi-four　model.　This　manuscript　aims　to　scrutinize　the　new　numerical　solution　of　the　nonlinear　time　fractional　Phi-four　equation　subject　to　nonhomogeneous　initial-boundary　conditions　by　means　of　cubic-B-spline　collocation　method　(CBSCM).　The　main　advantage　of　cubic　B-spline　method　over　existing　techniques　is　that　it　efficiently　provides　a　piecewise-continuous,　closed　form　solution　and　it　is　simpler　and　easy　to　apply　to　many　problems　involving　partial　differential　equations.　In　this　approach　the　fractional　differential　equation　is　converted　into　system　of　equations.　The　non-integer　derivative　＂alpha＂　is　considered　in　Caputo　sense.　The　discretization　of　Caputo　derivative　is　done　using　L1　formula,　while　B-spline　basis　functions　are　used　for　the　interpolation　of　spatial　derivative.　The　applicability　of　the　proposed　scheme　is　examined　on　two　test　problems.　The　influence　of　different　parameters　is　studied　and　captured　graphically　and　numerically.　The　proposed　scheme　is　proved　to　be　unconditionally　stable.　Moreover,　the　error　norms　are　computed　to　quantify　the　accuracy.