BF doesn't trust me

Alexis
My bf of 8 months that I've lived with for 4 months always thinks I'm snapchatting/texting other guys. I have never cheated on him and always let him check my phone if he wants bc I want him to trust me. Every gf before me cheated on him and he was a victim of child abuse so I get the trust issues, but I am 100% devoted to him. I just want him to trust me so we aren't always fighting. Help.