IMPACT OF THE SAME DEGENERATE ADDITIVE NOISE ON A COUPLED SYSTEM OF FRACTIONAL SPACE DIFFUSION EQUATIONS

References

• 1. I. R. Epstein and J. A. Pojman , An Introduction to Nonlinear Chemical Dynamics (Oxford University Press, 1998). Crossref, Google Scholar
• 2. K. Maginu , Reaction–Diffusion equation describing morphogenesis I waveform stability of stationary solutions in a one dimensional model, Math. Biosci. 27 (1975) 17–98. Crossref, Google Scholar
• 3. J. Murray , Mathematical Biology, II: Spatial Models and Biomedical Applications (Springer, 2003). Crossref, Google Scholar
• 4. A. M. Turing , The chemical basis of morphogenesis, Philos. Trans. Roy. Soc. B 237 (1952) 5–72. Crossref, Web of Science, Google Scholar
• 5. A. Esen, T. A. Sulaiman, H. Bulut and H. M. Baskonus , Optical solitons to the space-time fractional ($1+1$)-dimensional coupled nonlinear Schrödinger equation, Optik 167 (2018) 150–156. Crossref, Web of Science, Google Scholar
• 6. N. H. Sweilam, M. M. A. Hasan and D. Baleanu , New studies for general fractional financial models of awareness and trial advertising decisions, Chaos Solitons Fractals 104 (2017) 772–784. Crossref, Web of Science, Google Scholar
• 7. D. Baleanu, G. C. Wu and S. D. Zeng , Chaos analysis and asymptotic stability of generalized Caputo fractional differential equations, Chaos Solitons Fractals 102 (2017) 99–105. Crossref, Web of Science, Google Scholar
• 8. D. Y. Liu, O. Gibaru, W. Perruquetti and T. M. Laleg-Kirati , Fractional order differentiation by integration and error analysis in noisy environment, IEEE Trans. Autom. Control 60 (2015) 2945–2960. Crossref, Web of Science, Google Scholar
• 9. R. Caponetto, G. Dongola, L. Fortuna and A. Gallo , New results on the synthesis of FO-PID controllers, Commun. Nonlinear Sci. Numer. Simul. 15 (2010) 997–1007. Crossref, Web of Science, Google Scholar
• 10. A. Prakash, P. Veeresha, D. G. Prakasha and M. A. Goyal , Homotopy technique for fractional order multi-dimensional telegraph equation via Laplace transform, Eur. Phys. J. Plus 134 (2019) 1–18. Crossref, Web of Science, Google Scholar
• 11. P. Veeresha, D. G. Prakasha and H. M. Baskonus , New numerical surfaces to the mathematical model of cancer chemotherapy effect in Caputo fractional derivatives, Chaos 29 (2019) 013119. Crossref, Web of Science, Google Scholar
• 12. W. W. Mohammed , Fast-diffusion limit for reaction–diffusion equations with degenerate multiplicative and additive noise, J. Dyn. Differ. Equ. 33(1) (2021) 577–592. Crossref, Web of Science, Google Scholar
• 13. W. W. Mohammed, N. Iqbal, A. Ali and M. El-Morshedy , Exact solutions of the stochastic new coupled Konno–Oono equation, Results Phys. 21 (2021) 103830. Crossref, Web of Science, Google Scholar
• 14. W. W. Mohammed, S. Albosaily, N. Iqbal and M. El-Morshedy, The effect of multiplicative noise on the exact solutions of the stochastic Burgers’ equation, Waves Random Complex Media 1–13, doi:10.1080/17455030.2021.1905914. Google Scholar
• 15. D. Baleanu, B. Ghanbari, J. H. Asad, A. Jajarmi and H. M. Pirouz , Planar system-masses in an equilateral triangle: Numerical study within fractional calculus, CMES-Comput. Model. Eng. Sci. 124(3) (2020) 953–968. Web of Science, Google Scholar
• 16. D. Baleanu, S. S. Sajjadi, A. Jajarmi, O. Deferli and J. H. Asad , The fractional dynamics of a linear triatomic molecule, Roman. Rep. Phys. 73(1) (2021) 105. Web of Science, Google Scholar
• 17. D. Baleanu, S. S. Sajjadi, J. H. Asad, A. Jajarmi and E. Estiri , Hyperchaotic behaviors, optimal control, and synchronization of a nonautonomous cardiac conduction system, Adv. Differ. Equ. 2021 (2021) 157. Crossref, Web of Science, Google Scholar
• 18. D. Baleanu, S. S. Sajjadi, A. Jajarmi and Ö. Defterli , On a nonlinear dynamical system with both chaotic and non-chaotic behaviours: A new fractional analysis and control, Adv. Differ. Equ. 2021 (2021) 234. Crossref, Web of Science, Google Scholar
• 19. C. Prévôt and M. A. Röckner , A Concise Course on Stochastic Partial Differential Equations (Springer, 2007). Google Scholar
• 20. R. Gorenflo and F. Mainardi , Random walk models for space–fractional diffusion processes, Fract. Calc. Appl. Anal. 1 (1998) 167–191. Google Scholar
• 21. S. G. Samko, A. A. Kilbas and O. I. Marichev , Fractional Integrals and Derivatives: Theory and Applications (Gordon and Breach Science Publishers, 1993). Google Scholar
• 22. G. M. Zaslavsky, D. Stevens and H. Weitzner , Self-similar transport in incomplete chaos, Phys. Rev. E 48 (1993) 1683–1694. Crossref, Web of Science, Google Scholar
• 23. B. A. Carreras, V. E. Lynch and G. M. Zaslavsky , Anomalous diffusion and exit time distribution of particle tracers in plasma turbulence models, Phys. Plasmas 8 (2001) 5096–5103. Crossref, Web of Science, Google Scholar
• 24. M. F. Shlesinger, B. J. West and J. Klafter , Levy dynamics of enhanced diffusion: Application to turbulence, Phys. Rev. Lett. 58 (1987) 1100–1103. Crossref, Web of Science, Google Scholar
• 25. D. A. Benson, S. W. Wheatcraft and M. M. Meerschaeert , The fractional order governing equations of Levy motion, Water Resour. Res. 36 (2000) 1413–1423. Crossref, Web of Science, Google Scholar
• 26. M. M. Meerschaert, D. A. Benson and B. Baeumer , Multidimensional advection and fractional dispersion, Phys. Rev. E 59 (1999) 5026–5028. Crossref, Web of Science, Google Scholar
• 27. N. Iqbal, R. Wu and B. Liu , Pattern formation by super-diffusion in FitzHugh–Nagumo model, Appl. Math. Comput. 313 (2017) 245–258. Crossref, Web of Science, Google Scholar
• 28. N. Iqbal, R. Wu and W. W. Mohammed , Pattern formation induced by fractional cross-diffusion in a 3-species food chain model with harvesting, Math. Comput. Simul. 188 (2021) 102–119. Crossref, Web of Science, Google Scholar
• 29. N. Iqbal and Y. Karaca , Complex fractional-order HIV diffusion model based on amplitude equations with turing patterns and turing instability, Fractals 29 (2021) 2140013. Link, Web of Science, Google Scholar
• 30. W. W. Mohammed and D. Blömker , Fast-diffusion limit with large noise for systems of stochastic reaction–diffusion equations, Stoch. Anal. Appl. 34(6) (2016) 961–978. Crossref, Web of Science, Google Scholar
• 31. F. Liu, V. Anh, I. Turner and P. Zhuang , Numerical simulation for solute transport in fractal porous media, ANZIAM J. 45 (2004) 461–473. Crossref, Google Scholar
• 32. M. Ilic, F. Liu, I. Turner and V. Anh , Numerical approximation of a fractional-in-space diffusion equation, Fract. Calc. Appl. Anal. 8(3) (2005) 323–341. Google Scholar
• 33. M. Ilic, F. Liu, I. Turner and V. Anh , Numerical approximation of a fractional-in-space diffusion equation (II) — with nonhomogeneous boundary conditions, Fract. Calc. Appl. Anal. 9(4) (2006) 333–349. Google Scholar
• 34. S. Shen and F. Liu , Error analysis of an explicit finite difference approximation for space fractional diffusion, ANZIAM J. 46 (2005) 871–887. Crossref, Google Scholar
• 35. G. Da Prato and J. Zabczyk , Stochastic equations in infinite dimensions in Encyclopedia of Mathematics and Its Applications, Vol. 44 (Cambridge University Press, Cambridge, 1992). Crossref, Google Scholar
• 36. D. Blömker and W. W. Mohammed , Amplitude equations for SPDEs with cubic nonlinearities Stochastics, Int. J. Probab. Stoch. Process 85 (2013) 181–215. Crossref, Web of Science, Google Scholar
• 37. W. Wang, Q. Liu and Z. Jin , Spatiotemporal complexity of a ratio–dependent predator–prey system, Phys. Rev. E 75 (2007) 051913–051922. Crossref, Web of Science, Google Scholar
• 38. X. Zhang, G. Sun and Z. Jin , Spatial dynamics in a predator–prey model with Beddington–Deangelis functional response, Phys. Rev. E 85 (2012) 021924–021938. Crossref, Web of Science, Google Scholar
• 39. The MathWorks, MATLAB (R2019b), Natick The MathWorks, Inc. (2019). Google Scholar
• 40. S. V. Petrovskii and H. A. Malchow , Minimal model of pattern formation in a prey–predator system, Math. Comput. Model. 29 (1999) 49–63. Crossref, Web of Science, Google Scholar