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    Mathematical Analysis of Fractional Order Diarrhea Model
    (Natural Sciences Publishing, 2023) Ahmad, Aqeel; Farman, Muhammad; Akgül, Ali; Nissar, Kottakkaran Sooppy; Abdel-Aty, Abdel-Haleem
    In this paper, the Diarrhea system is analyzed to construct a scheme for the fractional-order mathematical model to see the actual behavior within the bounded domain. The fractional-order Diarrhea model is investigated with the Atangana-Toufik method. Different effects of Diarrhea in the system are presented to specify the dynamic nature of diarrhoea disease for different fractional values. Fixed point theory is used to derive the existence and unique solutions of the fractional order Diarrhea system. Positivity and boundedness for the proposed system are verified. The Atangana-Toufik method is an advanced category of fractional derivative which is used to obtain the bounded solution of the proposed system with a generalized Mittag-Leffler kernel. Simulations are derived for the proposed scheme to check the effectiveness of the results and to understand the effects of Diarrhea disease in society. Future predictions can also be easily made from the justified results obtained. The proposed system is also analyzed by using different fractional values to see the continuous monitoring of diarrhea disease. © 2023 NSP Natural Sciences Publishing Cor.
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    New Numerical Approach of Solving Highly Nonlinear Fractional Partial Differential Equations via Fractional Novel Analytical Method
    (Mdpi, 2022) Sultana, Mariam; Arshad, Uroosa; Abdel-Aty, Abdel-Haleem; Akgul, Ali; Mahmoud, Mona; Eleuch, Hichem
    In this work, the fractional novel analytic method (FNAM) is successfully implemented on some well-known, strongly nonlinear fractional partial differential equations (NFPDEs), and the results show the approach's efficiency. The main purpose is to show the method's strength on FPDEs by minimizing the calculation effort. The novel numerical approach has shown to be the simplest technique for obtaining the numerical solution to any form of the fractional partial differential equation (FPDE).