Toward the existence and uniqueness of solutions for fractional integro-differential equations under uncertainty

• Main Authors: Hosseini, Ali Ahmadian, Ismail, Fudziah, Senu, Norazak, Salahshour, Soheil, Suleiman, Mohamed
• Format: Conference or Workshop Item
• Language: English
• Published: AIP Publishing 2016
• Online Access: http://psasir.upm.edu.my/id/eprint/57180/1/Toward%20the%20existence%20and%20uniqueness%20of%20solutions%20for%20fractional%20integro-differential%20equations%20under%20uncertainty.pdf; http://psasir.upm.edu.my/id/eprint/57180/; http://aip.scitation.org/doi/abs/10.1063/1.4952514

The main contribution of the current paper is to obtain new results on the existence and uniqueness of the solution of fractional integro-differential equations under uncertainty with nonlocal conditions. For this purpose, we have used two basic tools, the contraction mapping principle and Krasnoselskii's fixed-point theorem. Indeed, we have considered the original problem involving fuzzy Caputo differentiability, together with fuzzy nonlinear condition.