**7. Conclusions**

A linearized difference scheme for solving a class of dmfCDWEs is constructed. With the help of an easy to execute and invertible exponential transformation, the considered problem can be converted into the delay variable coefficient fractional diffusion wave equation equivalently. Subsequently, we establish a fourth-order accurate numerical scheme that is based on a variable coefficient compact operator and with a temporal second order of convergence at a super-convergent point. The convergence and stability of the current numerical scheme are proved at length and a numerical example is finally added for the sake of demonstrating the theoretical findings.

**Author Contributions:** All authors contributed equally. All authors have read and agreed to the published version of the manuscript.

**Funding:** The first author wishes to acknowledge the support of RFBR Grant 19-01-00019.

**Acknowledgments:** The authors wish to thank the anonymous reviewers for their comments and criticism. All of their comments were taken into account in the revised version of the paper, resulting in a substantial improvement with respect to the original submission.

**Conflicts of Interest:** The authors declare no conflict of interest.

## **References**


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