Constructive Existence of (1,1)‎-Solutions to Two-Point Value Problems for Fuzzy Linear Multiterm Fractional Differential Equations

Abstract EN

In this paper, we consider the following two-point boundary value problems of fuzzy linear fractional differential equations: ( D c 1,1 α y ) ( t ) ⊕ b ( t ) ⊗ ( D c 1,1 β y ) ( t ) ⊕ c ( t ) ⊗ y ( t ) = f ( t ) , t ∈ ( 0,1 ) , y ( 0 ) = y 0 and y ( 1 ) = y 1 , where b , c ∈ C ( I ) , b ( t ) , c ( t ) ≥ 0 , y , f ∈ C ( I , R F ) , I = [ 0,1 ] , y 0 , y 1 ∈ R F and 1 < β < α ≤ 2 .

Our existence result is based on Banach fixed point theorem and the approximate solution of our problem is obtained by applying the Haar wavelet operational matrix.