On integral solutions of some nonlocal fractional differential equations with nondense domain (original) (raw)
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The boundary value problems of fractional differential equations involving Caputo derivatives are examined in this article. The ultimate goal of our study is to institute the existence and uniqueness properties for our boundary problems with nonlocal and integral boundary conditions by applying the Banach and the Schaefer's theorems of fixed point. We finally discuss two applicable questions to enhance the comprehension of our outcomes and conclude by summarizing our results and giving vital suggestions for further research works in relation to our study. I.
On Nonlocal Problems for Fractional Integro-Differential Equation in Banach Space
European Journal of Scientific Research, 2019
The aim of the present paper is to study the Cauchy-type problem for a integro-differential equation of fractional order with nonlocal conditions in Banach spaces. The fractional differential operator is taken in the Caputo sense. New conditions on the nonlinear terms are given to guarantee the equivalence. We shall prove the existence and uniqueness results by means of Banach fixed point and the Krasnoselskii's fixed point theorems. At the end, an illustrative example will be introduced to justify our results.