We investigate the existence and uniqueness of solutions for Hadamard fractional differential equations with nonlocal integral boundary conditions, by using the Leray-Schauder nonlinear alternative, Leray Schauder degree theorem, Krasnoselskiis fixed point theorem, Schaefers fixed point theorem, Banach fixed point theorem, Nonlinear Contractions. Two examples are also presented to illustrate our results.
<abstract><p>In this article, we investigate new results of existence and uniqueness for systems of nonlinear coupled differential equations and inclusions involving Caputo-type sequential derivatives of fractional order and along with new kinds of coupled discrete (multi-points) and fractional integral (Riemann-Liouville) boundary conditions. Our investigation is mainly based on the theorems of Schaefer, Banach, Covitz-Nadler, and nonlinear alternatives for Kakutani. The validity of the obtained results is demonstrated by numerical examples.</p></abstract>
In this article, we study the existence and uniqueness of solutions for nonlinear fractional integro-differential equations with nonlocal Erdélyi-Kober type integral boundary conditions. The existence results are based on Krasnoselskii’s and Schaefer’s fixed point theorems, whereas the uniqueness result is based on the contraction mapping principle. Examples illustrating the applicability of our main results are also constructed.
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