The　pioneering　work　in　finance　by　Black,　Scholes　and　Merton　during　the　1970s　led　to　the　emergence　of　the　Black-Scholes　(B-S)　equation,　which　offers　a　concise　and　transparent　formula　for　determining　the　theoretical　price　of　an　option.　The　establishment　of　the　B-S　equation,　however,　relies　on　a　set　of　rigorous　assumptions　that　give　rise　to　several　limitations.　The　non-local　property　of　the　fractional　derivative　(FD)　and　the　identification　of　fractal　characteristics　in　financial　markets　have　paved　the　way　for　the　introduction　and　rapid　development　of　fractional　calculus　in　finance.　In　comparison　to　the　classical　B-S　equation,　the　fractional　B-S　equations　(FBSEs)　offer　a　more　flexible　representation　of　market　behavior　by　incorporating　long-range　dependence,　heavy-tailed　and　leptokurtic　distributions,　as　well　as　multifractality.　This　enables　better　modeling　of　extreme　events　and　complex　market　phenomena,　The　fractional　B-S　equations　can　more　accurately　depict　the　price　fluctuations　in　actual　financial　markets,　thereby　providing　a　more　reliable　basis　for　derivative　pricing　and　risk　management.　This　paper　aims　to　offer　a　comprehensive　review　of　various　FBSEs　for　pricing　European　options,　including　associated　solution　techniques.　It　contributes　to　a　deeper　understanding　of　financial　model　development　and　its　practical　implications,　thereby　assisting　researchers　in　making　informed　decisions　about　the　most　suitable　approach　for　their　needs.　©　2024　by　the　authors.