There is a javascript function called execute_cells (see it on Github) that when given an list of cell indices runs those cells.
%%javascript
Jupyter.notebook.execute_cells([0]) # 0 to run first cell in notebook etc.
If you need to run it specifically in a Python code cell, one can use the Javascript function in the IPython.display module to execute javascript
from IPython.display import Javascript
Javascript("Jupyter.notebook.execute_cells([2])")
Note that this will move the cursor to executed cells. If you wish to get back to the cursor position, you may get the number of the next cell in order to execute it (code adapted from this answer) :
%%javascript
Jupyter.notebook.execute_cells([0]) # 0 to run first cell in notebook etc.
var output_area = this;
// find my cell element
var cell_element = output_area.element.parents('.cell');
// which cell is it?
var cell_idx = Jupyter.notebook.get_cell_elements().index(cell_element);
Jupyter.notebook.execute_cells([cell_idx+1]) # execute next cell