Abstract
In this paper, we investigate the existence and uniqueness of a coupled system of nonlinear fractional Langevin equations with nonseparated type integral boundary conditions. We use Banach’s and Krasnoselskii’s fixed point theorems to obtain the results. Lastly, we give two examples to show the effectiveness of the main results.
Highlights
In the recent few decades, fractional differential equations have been studied by many researchers, and this is due to the importance of this field and its applications in many problems of physics, chemistry, biology, and economy.In particular, fractional Langevin differential equations have been one of the important subjects in the field of fractional differential equations for their rich history
We have investigated the existence and uniqueness results for a coupled system of nonlinear fractional Langevin equations supplemented with nonseparated integral boundary conditions by using the Banach contraction principle and Krasnoselskii’s fixed point theorem
We gave two examples to prove the validity of our results
Summary
In the recent few decades, fractional differential equations have been studied by many researchers, and this is due to the importance of this field and its applications in many problems of physics, chemistry, biology, and economy (for more details, we refer the readers to [1,2,3,4,5,6] and many other references therein). E existence and uniqueness of the coupled system of nonlinear fractional Langevin equations with multipoint and nonlocal integral boundary conditions have been studied in [20]. In [19], the existence and uniqueness of solutions for a coupled system of Riemann–Liouville and Hadamard fractional derivatives of Langevin equation with fractional integral conditions were proved. To our knowledge, coupled fractional Langevin equations involving nonseparated type integral boundary conditions have not been extensively investigated yet.
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