Solving Fuzzy Fractional Differential Equations Using Zadeh's Extension Principle

Algorithm 1

Fuzzy fractional Euler method for a linear problem.

Input: Fractional Euler Equation, Fuzzy Initial Value, 𝛽, 𝑡₀, 𝑡_𝑁 and 𝑁

Descritise 𝛼←𝛼₀,𝛼₁,…,𝛼_𝑛;

𝑡ℎ←^𝑁−𝑡₀𝑁;

for  𝑗 = #(𝛼) do

  𝑤₁(1,𝑗)←𝑎+𝛼(𝑗)∗(𝑏−𝑎);

  𝑤₂(1,𝑗)←𝑐−𝛼(𝑗)∗(𝑐−𝑏);

end

for  𝑖=1 : 𝑁  do

  for  𝑗=1 : #(𝛼) do

    𝑤₁(𝑖+1,𝑗)←min(𝑔(𝛽,ℎ,𝑡_𝑖,𝑤₁(𝑖,𝑗)),𝑔(𝛽,ℎ,𝑡_𝑖,𝑤₂(𝑖,𝑗)));

    𝑤₂(𝑖+1,𝑗)←max(𝑔(𝛽,ℎ,𝑡_𝑖,𝑤₁(𝑖,𝑗)),𝑔(𝛽,ℎ,𝑡_𝑖,𝑤₂(𝑖,𝑗)));

  end

end

Output: 𝑤₁ and 𝑤₂