NDLI: Existence and Uniqueness of Solutions for Fractional Integro-Differential Equations Involving the Hadamard Derivatives

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Existence and Uniqueness of Solutions for Fractional Integro-Differential Equations Involving the Hadamard Derivatives

Content Provider	MDPI
Author	Nyamoradi, Nemat Ntouyas, Sotiris K. Tariboon, Jessada
Copyright Year	2022
Abstract	In this paper, we study the existence and uniqueness of solutions for the following fractional boundary value problem, consisting of the Hadamard fractional derivative: $_{H} D^{α} x (t) = A f (t, x (t)) + \sum_{i = 1}^{k} C_{i}_{H} I^{β_{i}} g_{i} (t, x (t)), t \in (1, e),$ supplemented with fractional Hadamard boundary conditions: $_{H} D^{ξ} x (1) = 0,_{H} D^{ξ} x (e) = a_{H} D^{\frac{α - ξ - 1}{2}} (_{H} D^{ξ} x (t)) \|_{t = δ}, δ \in (1, e),$ where $1 < α \leq 2$ , $0 < ξ \leq \frac{1}{2}$ , $a \in (0, \infty)$ , $1 < α - ξ < 2$ , $0 < β_{i} < 1$ , $A, C_{i}$ , $1 \leq i \leq k$ , are real constants, $_{H} D^{α}$ is the Hadamard fractional derivative of order $α$ and $_{H} I^{β_{i}}$ is the Hadamard fractional integral of order $β_{i}$ . By using some fixed point theorems, existence and uniqueness results are obtained. Finally, an example is given for demonstration.
Starting Page	3068
e-ISSN	22277390
DOI	10.3390/math10173068
Journal	Mathematics
Issue Number	17
Volume Number	10
Language	English
Publisher	MDPI
Publisher Date	2022-08-25
Access Restriction	Open
Subject Keyword	Mathematics Hardware and Architecturee Hadamard Fractional Derivative Existence and Uniqueness Fixed Point Theorems
Content Type	Text
Resource Type	Article

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