A new Weber-type integral transform and its inverse are defined for the representation of a function $f(r,t), (r,t)\in [R,1]\times [0,\infty )$ that satisfies the Dirichlet and Robin-type boundary conditions $f(R,t)=f_1(t)$, $f(1,t)-{\alpha \frac{\partial f(r,t)}{\partial r}|}_{r=1}=f_2(t)$, respectively. The orthogonality relations of the transform kernel are derived by using the properties of Bessel functions. The new Weber integral transform of some particular functions is determined. The integral transform defined in the present paper is a suitable tool for determining analytical solutions of transport problems with sliding phenomena that often occur in flows through micro channels, pipes or blood vessels. The heat conduction in an annular domain with Robin-type boundary conditions is studied. The subroutine $“root(\cdot )”$ of the Mathcad software is used to determine the positive roots of the transcendental equation involved in the definition of the new integral transform.

中文翻译：

---

具有罗宾型边界条件的韦伯型积分变换

为函数表示定义了新的Weber型积分变换及其逆 $F（\mathrm{[R}，Ť）， （\mathrm{[R}，Ť）\in [\mathrm{[R}，\mathrm{1个}]\times [0，\infty ）$ 满足Dirichlet和Robin型边界条件 $F（\mathrm{[R}，Ť）=F_{\mathrm{1个}}（Ť）$， $F（\mathrm{1个}，Ť）-{\alpha \frac{\partial F（\mathrm{[R}，Ť）}{\partial \mathrm{[R}}|}_{\mathrm{[R}=\mathrm{1个}}=F_2（Ť）$， 分别。利用贝塞尔函数的性质推导了变换核的正交关系。确定了某些特定函数的新Weber积分变换。本文定义的积分变换是确定带有滑动现象的运输问题的解析解决方案的合适工具，该问题经常发生在通过微通道，管道或血管的流动中。研究了具有罗宾型边界条件的环形区域内的热传导。子程序$“\mathrm{[R}ØØŤ（\cdot ）”$ Mathcad软件的“方程”用于确定新积分变换定义中所涉及的先验方程的正根。