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

Abstract

In this paper, we consider the following two-point boundary value problems of fuzzy linear fractional differential equations: (Dc1,1αy)(t)⊕b(t)⊗(Dc1,1βy)(t)⊕c(t)⊗y(t)=f(t), t∈(0,1), y(0)=y0 and y(1)=y1, where b,c∈C(I), b(t),c(t)≥0, y,f∈C(I,RF), I=[0,1], y0,y1∈RF 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.