文章基本信息

标题：Solutions of two fractional q -integro-differential equations under sum and integral boundary value conditions on a time scale
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作者：Jehad Alzabut ; Behnam Mohammadaliee ; Mohammad Esmael Samei 等
期刊名称：Advances in Difference Equations
印刷版ISSN：1687-1839
电子版ISSN：1687-1847
出版年度：2020
卷号：2020
期号：1
页码：1-33
DOI：10.1186/s13662-020-02766-y
出版社：Hindawi Publishing Corporation
摘要：In this manuscript, by using the Caputo and Riemann–Liouville type fractional q-derivatives, we consider two fractional q-integro-differential equations of the forms ${}^{c}\mathcal{D}_{q}^{\alpha }[x](t) + w_) (t, x(t), \varphi (x(t)) )=0$ and $$ {}^{c}\mathcal{D}_{q}^{\alpha }[x](t) = w_, \biggl( t, x(t), \int _(^{t} x(r) \,\mathrm{d}r, {}^{c} \mathcal{D}_{q}^{\alpha }[x](t) \biggr) $$ for $t \in [0,l]$ under sum and integral boundary value conditions on a time scale $\mathbb{T}_{t_(}= \{ t: t =t_(q^{n}\}\cup \{0\}$ for $n\in \mathbb{N}$ where $t_( \in \mathbb{R}$ and q in $(0,1)$. By employing the Banach contraction principle, sufficient conditions are established to ensure the existence of solutions for the addressed equations. Examples involving algorithms and illustrated graphs are presented to demonstrate the validity of our theoretical findings.
关键词：Sum boundary value conditions;Caputo q-derivative;Riemann–Liouville q-derivative;Integral boundary value conditions;