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DOI: 10.23952/cot.2020.1
Received August 19, 2019; Accepted December 17, 2019; Published January 13, 2020
Abstract. We study the existence and uniqueness of positive solutions of a fractional integro-differential equation with integral boundary conditions. We convert the given fractional integro-differential equation into an equivalent integral equation. Then we construct appropriate mappings and employ the Schauder fixed point theorem and the method of upper and lower solutions to show the existence of a positive solution. We also use the Banach fixed point theorem to show the existence of a unique positive solution. Finally, an example is given to illustrate our results.
How to Cite this Article:
Adel Lachouri, Abdelouaheb Ardjouni, Ahcene Djoudi, Positive solutions of a fractional integro-differential equation with integral boundary conditions, Communications in Optimization Theory, Vol. 2020 (2020), Article ID 1, pp. 1-9.