Mathematical study of Algae as a bio-fertilizer using fractal–fractional dynamic model

Abstract

Algae plays a vital role as bio-fertilizer and soil stabilizer in the field of agriculture. This paper considers a fractal–fractional dynamics model in sense of Caputo derivative that study the reuse of detritus generated by the dead algae as fertilizer for crop. In particular, we study dynamics model in which algae recovers nitrogen and phosphorus (waste nutrients) from water and is reused to enhance agricultural production. The theoretical results are established for the considered model with the aid of fixed point theory, whereas Ulam–Hyers approach is used for the stability of system. The numerical simulations are computed by using the well-known technique of fractional Adams–Bashforth. For simulation of the problem we consider different values for fractional order and fractal dimension by using some pre-existing data. Several graphical representation is given to understand the system at different fractional order and fractal dimension.