Novel Numerical Investigations of Fuzzy Cauchy Reaction–Diffusion Models via Generalized Fuzzy Fractional Derivative Operators

Fractal and Fractional

Manar A. Alqudah¹  Thabet Abdeljawad²  Saima Rashid³  Jagdev Singh⁴  Rehana Ashraf⁵  Zakia Hammouch⁶ 

[1] Department Mathematical Sciences, Faculty of Sciences, Princess Nourah Bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia;Department of Mathematics and General Sciences, Prince Sultan University, Riyadh 11586, Saudi Arabia;Department of Mathematics, Government College University, Faisalabad 38000, Pakistan;Department of Mathematics, JECRC University, Jaipur 303905, Rajasthan, India;Department of Mathematis, Lahore College for Women University, Lahore 54000, Pakistan;Ecole Normale Supéerieure de Meknés, Université Moulay Ismail, Meknes 50000, Morocco;

关键词: Shehu transform;    Caputo fractional derivative;    AB-fractional operator;    homotopy perturbation method;    Cauchy reaction–diffusion equation;   

DOI  :  10.3390/fractalfract5040151

来源: DOAJ

【 摘 要 】

The present research correlates with a fuzzy hybrid approach merged with a homotopy perturbation transform method known as the fuzzy Shehu homotopy perturbation transform method (SHPTM). With the aid of Caputo and Atangana–Baleanu under generalized Hukuhara differentiability, we illustrate the reliability of this scheme by obtaining fuzzy fractional Cauchy reaction–diffusion equations (CRDEs) with fuzzy initial conditions (ICs). Fractional CRDEs play a vital role in diffusion and instabilities may develop spatial phenomena such as pattern formation. By considering the fuzzy set theory, the proposed method enables the solution of the fuzzy linear CRDEs to be evaluated as a series of expressions in which the components can be efficiently identified and generating a pair of approximate solutions with the uncertainty parameter $\lambda \in [0,1].$ To demonstrate the usefulness and capabilities of the suggested methodology, several numerical examples are examined to validate convergence outcomes for the supplied problem. The simulation results reveal that the fuzzy SHPTM is a viable strategy for precisely and accurately analyzing the behavior of a proposed model.

【 授权许可】

Unknown