Existence and Location of a Unique Solution of Caputo-Liouville Type Langevin Equation with Finitely Many Nonlinearities and Nonlocal Boundary Conditions

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Bashir Ahmad
Ahmed Alsaedi
Hanan Al-Johany
Sotiris K. Ntouyas

Abstract

In this paper, we discuss the existence of a unique solution of Caputo-Liouville type Langevin equation involving two fractional orders and finitely many nonlinearities, equipped with nonlocal boundary conditions via Banach contraction mapping principle. The location of the unique solution of the given problem is also presented. In addition, we discuss the existence of solutions for the problem at hand by means of Krasnoselskii's fixed point theorem. Examples are constructed for the illustration of the obtained results. The paper concludes with some interesting remarks.

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