Infinite system of nonlinear tempered fractional order BVPs in tempered sequence spaces

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2024年2月1日

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Sabbavarapu Nageswara Rao,
Mahammad Khuddush,
Ahmed Hussein Msmali,
Abdullah Ali H. Ahmadini

摘要

This paper deals with the existence results of the infinite system of tempered fractional BVPs $\begin{matrix} {}_{0}^{R}D_{r}^{ϱ, λ} z_{j} (r) + ψ_{j} (r, z (r)) = 0, 0 < r < 1, \\ z_{j} (0) = 0,_{0}^{R} D_{r}^{m, λ} z_{j} (0) = 0, \\ b_{1} z_{j} (1) + {b_{2}}_{0}^{R} D_{r}^{m, λ} z_{j} (1) = 0, \end{matrix}$ $\begin{aligned}& {}^{\mathtt{R}}_{0}\mathrm{D}_{\mathrm{r}}^{\varrho , \uplambda} \mathtt{z}_{\mathtt{j}}(\mathrm{r})+\psi _{\mathtt{j}}\bigl(\mathrm{r}, \mathtt{z}(\mathrm{r})\bigr)=0,\quad 0< \mathrm{r}< 1, \\& \mathtt{z}_{\mathtt{j}}(0)=0,\qquad {}^{\mathtt{R}}_{0} \mathrm{D}_{ \mathrm{r}}^{\mathtt{m}, \uplambda} \mathtt{z}_{\mathtt{j}}(0)=0, \\& \mathtt{b}_{1} \mathtt{z}_{\mathtt{j}}(1)+\mathtt{b}_{2} {}^{ \mathtt{R}}_{0}\mathrm{D}_{\mathrm{r}}^{\mathtt{m}, \uplambda} \mathtt{z}_{\mathtt{j}}(1)=0, \end{aligned}$ where $j \in N$ $\mathtt{j}\in \mathbb{N}$ , $2 < ϱ \leq 3$ $2<\varrho \le 3$ , $1 < m \leq 2$ $1<\mathtt{m}\le 2$ , by utilizing the Hausdorff measure of noncompactness and Meir–Keeler fixed point theorem in a tempered sequence space.