A new technique to solve the initial value problems for fractional fuzzy delay differential equations

• Main Authors: Truong Vinh An, Ho Vu, Ngo Van Hoa
• Format: Article
• Language: English
• Published: SpringerOpen 2017-06-01
• Series: Advances in Difference Equations
• Subjects: fractional interval-valued differential equations; fractional interval-valued delay differential equations; weakly contractive mapping
• Online Access: http://link.springer.com/article/10.1186/s13662-017-1233-z

Abstract Using some recent results of fixed point of weakly contractive mappings on the partially ordered space, the existence and uniqueness of solution for interval fractional delay differential equations (IFDDEs) in the setting of the Caputo generalized Hukuhara fractional differentiability are studied. The dependence of the solution on the order and the initial condition of IFDDE is shown. A new technique is proposed to find the exact solutions of IFDDE by using the solutions of interval integer order delay differential equation. Finally, some examples are given to illustrate the applications of our results.