This takes some explanation.
Plants grow by photosynthesizing. In order to photosynthesize, there has to be sufficient light (intensity and spectrum factor in) along with the necessary 17 nutrients in sufficient quantity to balance the light. And each species of plant has its own specific requirement for this balance; fast growing plants require more, slow-growing plants less, generally.
Light is thus the most crucial factor, as it must be of a certain intensity and spectrum to drive photosynthesis. Duration does not compensate for inadequate intensity/spectrum. So assuming the light is "OK," we can consider the nutrients which is the substance of your question.
Fish excrete all the nutrients plants need. There is also the breakdown of organics primarily in the substrate which adds more (especially the CO2). Water changes replenish the minerals (except obviously in very soft water) as well as removing substances that are detrimental to plants and others detrimental to fish. Depending upon the plant species and numbers, the light, and the fish load, some plants will manage very well just from the aforementioned.
If it is necessary to supplement any of these nutrients, it is important to do so with a balanced "fertilizer." An excess of some nutrients can cause plants to shut down assimilation of certain other nutrients; the excess can also feed algae because algae is not as fussy as higher plants over light and balanced nutrients. This is why comprehensive supplements are best; they provide what the plants need as a supplement to what will naturally occur in the aquarium, but the nutrients are in specific proportions to each other. Algae is much less likely to take advantage, because the plants are able to use what is being provided...again assuming everything is basically in balance.
Some plants benefit from substrate supplementation with products like Flourish Tabs as opposed to a liquid fertilizer. The real benefit here is that the plants can utilize the nutrients as needed while the nutrients are not just released into the water where algae may use them.
Comprehensive supplements include Seachem's Flourish Comprehensive Supplement for the Planted Aquarium, and Brightwell Aquatics' FlorinMulti. These are two I have looked into and used, but I'm sure they may be others. However, do not resort to individual nutrients; usually this is not going to benefit because it throws the balance out. The complete supplemental products contain what is needed in proportion as needed by plants, so unless you overdose (or under-dose), algae is not going to benefit.