This manuscript deals with a regularization technique for a generalized space-fractional backward heat conduction problem (BHCP) which is well-known to be extremely ill-posed. The presented technique is developed based on the Meyer wavelets in retrieving the solution of the presented space-fractional BHCP. Some sharp optimal estimates of the Hölder-Logarithmic type are theoretically derived by imposing an a-priori bound assumption via the Sobolev scale. The existence, uniqueness and stability of the considered problem are rigorously investigated. The asymptotic error estimates for both linear and non-linear problems are all the same. Finally, the performance of the proposed technique is demonstrated through one- and two-dimensional prototype examples that validate our theoretical analysis. Furthermore, comparative results verify that the proposed method is more effective than the other existing methods in the literature.

该手稿涉及一种正则化技术，用于解决众所周知的病态严重的广义空间分形向后导热问题（BHCP）。提出的技术是基于Meyer小波开发的，用于检索提出的空间分数BHCP的解。理论上，通过Sobolev量表施加先验约束假设，可以得出一些Hölder-对数类型的精确估计。认真研究了所考虑问题的存在性，唯一性和稳定性。线性和非线性问题的渐近误差估计都相同。最后，通过一维和二维原型实例证明了所提出技术的性能，这些实例验证了我们的理论分析。此外，