JavaScript (Node.js), 41 bytes

A port of xnor's answer. Takes input as a BigInt literal.

f=(n,a=1n,b=a)=>n&&n%10n*b+f(n/10n,b,a+b)

Try it online!

#JavaScript (ES6), 44 bytes

Takes input as an array of characters, in LSB-first order.

s=>s.map(k=>t+=k*(z=x,x=y,y+=z),x=t=0,y=1)|t

Try it online!

JavaScript (Node.js), 41 bytes

A port of xnor's answer. Takes input as a BigInt literal.

f=(n,a=1n,b=a)=>n&&n%10n*b+f(n/10n,b,a+b)

Try it online!

JavaScript (ES6), 44 bytes

Takes input as an array of characters, in LSB-first order.

s=>s.map(k=>t+=k*(z=x,x=y,y+=z),x=t=0,y=1)|t

Try it online!

JavaScript (Node.js), 41 bytes

A port of xnor's answer. Takes input as a BigInt literal.

f=(n,a=1n,b=a)=>n&&n%10n*b+f(n/10n,b,a+b)

Try it online!

#JavaScript (ES6), 54 bytes

Takes input as an array of characters.

s=>s.reverse().map(k=>t+=k*(z=x,x=y,y+=z),x=t=0,y=1)|t

Try it online!

JavaScript (Node.js), 41 bytes

A port of xnor's answer. Takes input as a BigInt literal.

f=(n,a=1n,b=a)=>n&&n%10n*b+f(n/10n,b,a+b)

Try it online!

#JavaScript (ES6), 44 bytes

Takes input as an array of characters, in LSB-first order.

s=>s.map(k=>t+=k*(z=x,x=y,y+=z),x=t=0,y=1)|t

Try it online!