برﺭﺳﻲ ﻭﺟﻮﺩ ﺟﻮﺍﺏ ﺑﺮﺍﻱ ﻣﻌﺎﺩﻟﻪ ﺍﻧﺘﮕﺮﺍﻟﻲ ﮐﺴﺮﻱ ﺑﺎ ﺍﺳﺘﻔﺎﺩﻩ ﺍﺯ ﺍﻧﺪﺍﺯﻩ ﻧﺎﻓﺸﺮﺩﮔﻲ ﺩﺭ ﻓﻀﺎﻱ ﺑﺎﻧﺎﺥ

On the existence of solutions for fractional integral equations by measure of non-compactness in Banach space

ﺩﺭ ﺍﻳﻦ ﻣﻘﺎﻟﻪ، ﻭﺟﻮﺩ ﺟﻮﺍﺏ ﺑﺮﺍﻱ ﺩﺳﺘﻪ ﺍﻱ ﺍﺯ ﻣﻌﺎﺩﻻﺕ ﺍﻧﺘﮕﺮﺍﻟﻲ ﻏﻴﺮ ﺧﻄﻲ ﮐﺴﺮﻱ ﺩﺭ ﻓﻀﺎﻱ ﺑﺎﻧﺎﺥ ﻣﻮﺭﺩ ﺑﺮﺭﺳﻲ ﻗﺮﺍﺭ ﻣﻲ ﮔﻴﺮﺩ. ﺍﺑﺰﺍﺭﻫﺎﻱ ﺍﺻﻠﻲ ﻣﻮﺭﺩ ﻧﻴﺎﺯ، ﺗﮑﻨﻴﮏ ﺍﻧﺪﺍﺯﻩ ﻧﺎ ﻓﺸﺮﺩﮔﻲ ﻭ ﻗﻀﻴﻪ ﻧﻘﻄﻪ ﺛﺎﺑﺖ ﭘﺘﺮﺷﻦ ﻣﻲ ﺑﺎﺷﻨﺪ. ﻫﻤﭽﻨﻴﻦ، ﺑﻪ ﻣﻨﻈﻮﺭ ﻧﺸﺎﻥ ﺩﺍﺩﻥ ﮐﺎﺭﺑﺮﺩﻱ ﺑﻮﺩﻥ ﻧﺘﺎﻳﺞ ، ﭼﻨﺪ ﻣﺜﺎﻝ ﺍﺭﺍﺋﻪ ﺷﺪﻩ ﺍﺳﺖ.

n this paper, the existence of the solutions of a class of fractional integral equations in Banach algebra, are investigated. The main tools here are the technique of the measure of noncompactness and the Petryshyn's fixed point theorem. Also, for the applicability of the obtained results, some examples are given.