ABSTRACT

This paper is introduced as complementary studies based on fractional Sturm–Liouville problems in a Banach space. We explore the existence results for new considered problems which can be considered as mixture of equations and inclusions. For the sake of that, we use jointly continuous composed functions with multi-valued maps and denote this form by eq-inclusion problems. The form of the solutions is calculated by the rules of Caputo derivative and the corresponding integral. The concept “continuous image of multi-valued maps” is useful to show that the strong results will be under inclusion hypothesis. The argument and fit technicals used here consider both Lipschitz and non-Lipschitz cases with using nonlinear alternative Leray Schauder type and Covitiz and Nadler theorems.

摘要

本文是基于Banach空间中分数Sturm-Liouville问题的补充研究而介绍的。我们探索了新考虑的问题的存在性结果，这些问题可以视为方程和包含项的混合。因此，我们将联合连续组合函数与多值映射一起使用，并通过等式-包含问题来表示这种形式。解的形式由Caputo导数规则和相应的积分计算。“多值地图的连续图像”概念可用于表明强结果将在包含假设下。这里使用的论证和拟合技术考虑了使用非线性替代Leray Schauder类型以及Covitiz和Nadler定理的Lipschitz和非Lipschitz情况。