Variational Iteration Transform Method for Fractional Differential Equations with Local Fractional Derivative

Table 1

Original function	Transformed function
𝑓(𝑥)=𝑥^𝑚𝛼	𝐹(𝑘)=1,𝑘=𝑚0,𝑘≠𝑚
𝑢(𝑥)𝑣(𝑥)	^𝑘∑𝑟=0{𝑈(𝑟)𝑉(𝑘−𝑟)}
𝑢^(𝑚𝛼)(𝑥)	Γ[1+(𝑘+𝑚)𝛼]Γ()𝑈()1+𝑘𝛼𝑘+𝑚;𝑘≥−𝑚+1
𝑓(𝑥)=0𝐼^𝛼𝑥⋯0𝐼^𝛼𝑥𝑘0𝑢(𝜏)	𝐹(𝑘)=Γ1+𝑘−𝑘0𝛼Γ()𝑈1+𝑘𝛼𝑘−𝑘0