DESIGN AND IMPLEMENTATION OF FUZZY-FRACTIONAL WU–ZHANG SYSTEM USING HE–MOHAND ALGORITHM

Mubashir Qayyum, Efaza Ahmad, Muhammad Sohail, Nadia Sarhan, Emad Mahrous Awwad and Amjad Iqbal
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Mubashir Qayyum: Department of Sciences and Humanities, National University of Computer and Emerging Sciences, Lahore, Pakistan
Efaza Ahmad: Department of Sciences and Humanities, National University of Computer and Emerging Sciences, Lahore, Pakistan
Muhammad Sohail: ��Institute of Mathematics, Khwaja Fareed University of Engineering and Information Technology, Rahim Yar Khan 64200, Pakistan
Nadia Sarhan: ��Department of Quantitative Analysis, College of Business Administration, King Saud University, Riyadh, Saudi Arabia
Emad Mahrous Awwad: �Department of Electrical Engineering, College of Engineering, King Saud University, P. O. Box 800, Riyadh 11421, Saudi Arabia
Amjad Iqbal: �Faculty of Materials Engineering, Silesian University of Technology, Gliwice 44-100, Poland

FRACTALS (fractals), 2024, vol. 32, issue 07n08, 1-17

Abstract: In recent years, fuzzy and fractional calculus are utilized for simulating complex models with uncertainty and memory effects. This study is focused on fuzzy-fractional modeling of (2+1)-dimensional Wu–Zhang (WZ) system. Caputo-type time-fractional derivative and triangular fuzzy numbers are employed in the model to observe uncertainties in the presence of non-local and memory effects. The extended He–Mohand algorithm is proposed for the solution and analysis of the current model. This approach is based on homotopy perturbation method along with Mohand transformation. Effectiveness of proposed methodology at upper and lower bounds is confirmed through residual errors. The theoretical convergence of proposed algorithm is proved alongside numerical computations. Existence and uniqueness of solution are also theoretically proved in the given paper. Current investigation considers three types of fuzzifications i.e. fuzzified equations, fuzzified conditions, and finally fuzzification in both model and conditions. Different physical aspects of WZ system profiles are analyzed through 2D and 3D illustrations at upper and lower bounds. The obtained results highlight the impact of uncertainty on WZ system in fuzzy-fractional space. Hence, the proposed methodology can be used for other fuzzy-fractional systems for better accuracy with lesser computational cost.

Keywords: Fuzzy-Fractional Model; Caputo Derivative; Triangular Fuzzy Number; Wu–Zhang System; Mohand Transform; Homotopy Perturbation (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1142/S0218348X24400322

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