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Fractional order model for yield through diagnosed/undiagnosed soil

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Abstract

Farming is the basic economy of any country. Soil fertility and water are key resources for yielding. The fractional order compartmental model is prepared in Caputo sense to improve the density of yield through diagnosed and undiagnosed soil. To measure the growing intensity of yield, the basic reproduction number is formulated using the next generation matrix method for integer order non-linear dynamical system. Local stability analysis is described for both the equilibrium points; undiagnosed soil free and optimum equilibrium point. Global stability is exhaustively computed by generating a Lyapunov function. With reference to the basic reproduction number, bifurcation analysis has been defined which expresses the chaotic nature of soil fertility. Moreover, optimal control theory is applied in the present fractional model to optimize yield. And optimality conditions are calculated with the help of Pontryagin maximum principle. The numerical simulation for different fractional orders is performed concerning validated data to analyze the behavior with respect to the order.

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Acknowledgements

All authors are thankful to DST-FIST file # MSI-097 for technical support to the department of Gujarat University. Second author (ENJ) is funded by UGC granted National Fellowship for Other Backward Classes (NFO-2018-19-OBC-GUJ-71790). Third author (PMP) is funded a scholarship by the Education Department, Gujarat state under the Scheme of Develo** High quality research.

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  1. Department of Mathematics, Gujarat University, Ahmedabad, Gujarat, 380009, India

    Nita H. Shah, Ekta N. Jayswal & Purvi M. Pandya

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  1. Nita H. Shah
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  2. Ekta N. Jayswal
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  3. Purvi M. Pandya
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Correspondence to Nita H. Shah.

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Communicated by José Alberto Cuminato.

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Shah, N.H., Jayswal, E.N. & Pandya, P.M. Fractional order model for yield through diagnosed/undiagnosed soil. São Paulo J. Math. Sci. 15, 392–403 (2021). https://doi.org/10.1007/s40863-020-00198-w

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