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Applications of contractive-like mapping principles to interval-valued fractional integro-differential equations

Authors: 

Truong Vinh An, Ngo Van Hoa*, Ho Vu

Source title: 
Journal of Fixed Point Theory and Applications, 19: 2577-2599, 2017 (ISI)
Academic year of acceptance: 
2017-2018
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 integro-differential equations (IFIDEs) 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 IFIDE is shown. A new technique is proposed to find the exact solutions of IFIDE by using the solutions of interval integer order integro-differential equation. Finally, an example is given to illustrate the applications of our results.