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: $({{}^{c}D}_{\mathrm{1,1}}^{\alpha }y)(t)\oplus b(t)\otimes ({{}^{c}D}_{\mathrm{1,1}}^{\beta }y)(t)\oplus c(t)\otimes y(t)=f(t)$, $t\in (\mathrm{0,1})$, $y(\mathrm{0})=y_{\mathrm{0}}$ and $y(\mathrm{1})=y_{\mathrm{1}}$, where $b,c\in C(I)$, $b(t),c(t)\ge \mathrm{0}$, $y,f\in C(I,{\mathbf{R}}_{\mathrm{F}})$, $I=[\mathrm{0,1}]$, $y_{\mathrm{0}},y_{\mathrm{1}}\in {\mathbf{R}}_{\mathrm{F}}$ and . 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.