No. The PSP (PlayStation Portable) and Nintendo systems (DS, 3DS, Switch, Game Boy, etc.) are completely incompatible platforms.
| Aspect | PSP | Nintendo (DS/3DS/Switch) |
|---|---|---|
| CPU Architecture | MIPS (Allegrex) / ARM (Media Engine) | ARM (ARM9/ARM11/Cortex-A57) |
| Media | UMD (optical), Memory Stick, Digital | Game Card (cartridge), SD/microSD, Digital |
| OS / SDK | Proprietary (PSP OS) | Proprietary (Nintendo SDK) |
| Binary Format | ELF / PRX / PBP | NRO / NCA / CIAs / .nds / .3ds |
To play Nintendo games, buy Nintendo hardware. To play PSP games, buy PSP (or Vita/PS TV/PC via PPSSPP).