Purpose　-　This　paper　aims　to　apply　fractional　variational　iteration　method　using　He＇s　polynomials　(FVIMHP)　to　obtain　exact　solutions　for　variable-coefficient　fractional　heat-like　and　wave-like　equations　with　fractional　order　initial　and　boundary　conditions.　Design/methodology/approach　-　The　approach　is　based　on　FVIMHP.　The　authors　choose　as　some　examples　to　illustrate　the　validity　and　the　advantages　of　the　method.　Findings　-　The　results　reveal　that　the　FVIMHP　method　provides　a　very　effective,　convenient　and　powerful　mathematical　tool　for　solving　fractional　differential　equations.　Originality/value　-　The　variable-coefficient　fractional　heat-like　and　wave-like　equations　with　fractional　order　initial　and　boundary　conditions　are　solved　first.　Illustrative　examples　are　included　to　demonstrate　the　validity　and　applicability　of　the　method.