Etkili yöntem kullanan ağ erişim kontrolü modeli için kesirli yaklaşım

Öz

Bu makalede, kesirli doğal ayrıştırma yöntemi (FNDM) kullanarak ağ erişim kontrolünde ortaya çıkan kesirli mertebeye sahip doğrusal olmayan adi diferansiyel denklemler sistemi için çözüm buluyoruz. Sensör ağlarını göstermek için kullanılan ve beş doğrusal olmayan adi diferansiyel denklem (NODE) sisteminden oluşan bu model, bütünlüğü, kullanılabilirliği ve gizliliği azaltmak amacıyla ağa saldıranlar için ilginç temel özelliklere sahiptir. Ayrıca, grafikler açısından farklı kesirli parametre değerleri için FNDM çözümlerinin grafiklerini de çizdik. Dikkate alınan method, doğrusal olmayan modelleri incelerken oldukça etkili ve yapılandırılmıştır ve elde edilen sonuçlardan gözlemlenebilir ve doğrulanabilirdir. Üstelik, grafiklerden elde edilen verilerden, kesirli operatörlerin, gerçek dünya problemlerinin kaydadeğer özelliklerini ortaya çıkarmak için oldukça yardımedebilir olduğu doğrulanır.

Anahtar Kelimeler

• Caputo türevi
• ağ erişim kontrol model
• matematiksel model
• kesirli natural ayrıştırma yöntemi.

Fractional approach for model of network access control using efficient method

Öz

In this paper, we find the solution for the system of nonlinear ordinary differential equations having fractional-order arising in network access control using fractional natural decomposition method (FNDM). The consider a model which consists of a system of five nonlinear ordinary differential equations (NODEs), which illustrate the sensor networks are interesting essentials for malicious outbreaks that attack the network with the intention of reducing the integrity, availability and confidentiality. Further, we captured the nature of FNDM results for different value of fractional order in terms of the plots. The considered scheme highly effective and structured while examining nonlinear models and which can be observed and confirm from the obtained results. Further, the conspiracies cited in plots confirm the hired fractional operator and algorithm can help to exemplify the more fascinating properties of the nonlinear system associated real-world problems.

Anahtar Kelimeler

• Caputo derivative
• network access control
• mathematical model
• fractional natural decomposition method.

Kaynakça

1. Caputo, M., Elasticita e Dissipazione, Zanichelli, Bologna, (1969).
2. Miller, K. S. and Ross, B., An introduction to fractional calculus and fractional differential equations, A Wiley, New York, (1993).
3. Podlubny, I., Fractional Differential Equations, Academic Press, New York, (1999).
4. Kilbas, A. A., Srivastava, H. M. and Trujillo, J. J., Theory and applications of fractional differential equations, Elsevier, Amsterdam, (2006).
5. Baleanu, D., Guvenc, Z. B. and Machado, T. J. A., New trends in nanotechnology and fractional calculus applications, Springer Dordrecht Heidelberg, London New York, (2010).
6. Prakasha, D. G. and Veeresha, P., Analysis of Lakes pollution model with Mittag-Leffler kernel, J. Ocean Eng. Sci., 5 (4), 310-322, (2020).
7. Baleanu, D., Wu, G. C. and Zeng, S. D., Chaos analysis and asymptotic stability of generalized Caputo fractional differential equations, Chaos Solitons Fractals, 102, 99-105, (2017).
8. Veeresha, P., Prakasha, D. G. and Baskonus, H. M., New numerical surfaces to the mathematical model of cancer chemotherapy effect in Caputo fractional derivatives, Chaos, 29, (013119), (2019).

9. Baskonus, H. M., Sulaiman, T. A. and Bulut, H., On the new wave behavior to the Klein-Gordon-Zakharov equations in plasma physics, Indian J. Phys., 93, (3), 393-399, (2019).
10. Veeresha, P. and Prakasha, D. G., Solution for fractional generalized Zakharov equations with Mittag-Leffler function, Results Eng., 5, 1-12, (2020).
11. Prakasha, D. G., Malagi, N. S. and Veeresha, P., New approach for fractional Schrödinger–Boussinesq equations with Mittag-Leffler kernel, Math. Meth. Appl. Sci., (2020).
12. Gao, W., Baskonus, H. M. and Shi, L., New investigation of Bats-Hosts-Reservoir-People coronavirus model and apply to 2019-nCoV system, Adv. Differ. Equ., 391, (2020).
13. Cattani, C. and Pierro, G., On the fractal geometry of DNA by the binary image analysis, Bull. Math. Biol., 75, (9), 1544-1570, (2013).
14. Gao, W., Veeresha, P., Prakasha, D. G. and Baskonus, H.M., Novel dynamical structures of 2019-nCoV with nonlocal operator via powerful computational technique, Biology, 9, (5), (2020).
15. Gao, W., Veeresha, P., Baskonus, H. M., Prakasha, D. G. and Kumar, P., A new study of unreported cases of 2019-nCOV epidemic outbreaks, Chaos Solitons Fractals, 138, (2020).
16. Cattani, C., Haar wavelet-based technique for sharp jumps classification, Math. Comput. Model., 39, (2-3), 255-278, (2004).
17. Gao, W., Yel, G., Baskonus, H.M. and Cattani, C., Complex solitons in the conformable (2+1)-dimensional Ablowitz-Kaup-Newell-Segur equation, AIMS Math., 5, (1), 507–521, (2020).
18. Al-Ghafri, K. S. and Rezazadeh, H., Solitons and other solutions of (3+1)-dimensional space–time fractional modified KdV–Zakharov–Kuznetsov equation, Appl. Math. Nonlinear Sci., 4, (2), 289-304, (2019).
19. Dananea, J., Allalia, K. and Hammouch, Z., Mathematical analysis of a fractional differential model of HBV infection with antibody immune response, Chaos Solitons Fractals, 136, 109787, (2020).
20. Singh, J., Kumar, D., Hammouch, Z. and Atangana, A., A fractional epidemiological model for computer viruses pertaining to a new fractional derivative, Appl. Math. Comput., 316, 504-515, (2018).
21. Ravichandran, C., Logeswari, K. and Jarad, F., New results on existence in the framework of Atangana–Baleanu derivative for fractional integro-differential equations, Chaos Solitons Fractals, 125, 194-200, (2019).
22. Veeresha, P., Prakasha, D. G. and Baskonus, H. M., An efficient technique for coupled fractional Whitham-Broer-Kaup equations describing the propagation of shallow water waves, Advances in Intelligent Systems and Computing, 49-75, (2020).
23. Kiran, M. S., et al., A mathematical analysis of ongoing outbreak COVID‐19 in India through nonsingular derivative, Numer. Meth. Partial Differ. Equ., (2020), DOI: 10.1002/num.22579.
24. Veeresha, P., Prakasha, D. G., Singh, J., Kumar, D. and Baleanu, D., Fractional Klein-Gordon-Schrödinger equations with Mittag-Leffler memory, Chinese J. Phy., 68, 65-78, (2020).
25. Subashini, R., Ravichandran, C., Jothimani, K. and Baskonus, H. M., Existence results of Hilfer integro-differential equations with fractional order, Discrete Contin. Dyn. Syst. Ser. S, 13, (3), 911-923, (2020).
26. Veeresha, P. and Prakasha, D. G. Novel approach for modified forms of Camassa–Holm and Degasperis–Procesi equations using fractional operator, Commun. Theor. Phys., 72, (10) (2020),
27. Panda, S. K., Abdeljawad, T. and Ravichandran, C., Novel fixed point approach to Atangana-Baleanu fractional and Lp-Fredholm integral equations, Alexandria Eng. J., 59, (4), 1959-1970, (2020).
28. Veeresha, P., Prakasha, D. G. and Hammouch, Z., An efficient approach for the model of thrombin receptor activation mechanism with Mittag-Leffler function, Nonlinear Analysis: Problems, Applications and Computational Methods, 44-60, (2020).
29. Subashini, R., Jothimani, K., Nisar, K. S. and Ravichandran, C. New results on nonlocal functional integro-differential equations via Hilfer fractional derivative, Alexandria Eng. J., 59, (5), 2891-2899, (2020).
30. Alqudah, M. A., Ravichandran, C., Abdeljawad, T. and Valliammal, N., New results on Caputo fractional-order neutral differential inclusions without compactness, Adv. Differ. Equ., 528, (2019).
31. Veeresha, P., Prakasha, D. G. and Baleanu, D., Analysis of fractional Swift-Hohenberg equation using a novel computational technique, Math. Meth. Appl. Sci., 43, (4), 1970-1987, (2020).
32. Logeswari, K. and Ravichandran, C., A new exploration on existence of fractional neutral integro-differential equations in the concept of Atangana–Baleanu derivative, Phys. A, 544, (2020), DOI: 10.1016/j.physa.2019.123454
33. Veeresha, P., Prakasha, D. G. and Kumar, D., Fractional SIR epidemic model of childhood disease with Mittag-Leffler memory, Fractional Calculus in Medical and Health Science, 229-248, (2020).
34. Akyildiz, I. F., Su, W., Sankarasubramaniam, Y. and Cayirci, E., Wireless sensor networks: A survey, Computer Networks, 38, (4), 393–422, (2002).
35. Nwokoye, C. H., Umeh, I., Nwanze, M. and Alao, B. F., Analyzing time delay and sensor distribution in sensor networks, IEEE African Journal of Computing & ICT 8, 1, 159–164, (2015).
36. Giannetsos, T., Dimitriou, T. and Prasad, N. R., Self-propagating worms in wireless sensor networks, ACM CoNEXT-Student Workshop’09, 31–32, (2009).
37. Gupta, A. and Gupta, A. K., A survey: Detection and prevention of wormhole attack in wireless sensor networks, Global Journal of Computer Science and Technology: E Network, Web & Security, 14, 23–31, (2014).
38. ChukwuNonso, H. N., Mbeledogu, N., Umeh, I. I., Ihekeremma, and Ejimofor, A., Modeling the effect of network access control and sensor random distribution on worm propagation, I.J. Modern Education and Computer Science, 11, 49-57, (2017).
39. Adomian, G., A new approach to nonlinear partial differential equations, J. Math. Anal. Appl., 102, 420-434, (1984).
40. Khan, Z. H. and Khan, W. A., N-Transform-properties and applications, NUST J. Engg. Sci., 1, (1), 127-133, (2008).
41. Rawashdeh, M. S., The fractional natural decomposition method: theories and applications, Math. Meth. Appl. Sci., 40, 2362-2376, (2017).
42. Rawashdeh, M. S. and Maitama, S., Finding exact solutions of nonlinear PDEs using the natural decomposition method, Math. Meth. Appl. Sci., 40, 223-236, (2017).
43. Prakasha, D. G., Veeresha, P. and Rawashdeh, M. S., Numerical solution for (2+1)‐dimensional time‐fractional coupled Burger equations using fractional natural decomposition method, Math. Meth. Appl. Sci., 42, (10), 3409-3427, (2019).
44. Veeresha, P., Prakasha, D.G. and Singh, J., Solution for fractional forced KdV equation using fractional natural decomposition method, AIMS Math., 5, (2), 798-810, (2019).
45. Rawashdeh, M. S., Solving fractional ordinary differential equations using FNDM, Thai Journal of Mathematics, 17, (1), 239–251, (2019).
46. Prakasha, D. G., Veeresha, P. and Baskonus, H. M., Two novel computational techniques for fractional Gardner and Cahn‐Hilliard equations, Comp. Math. Methods, 1, (2), 1-19, (2019).
47. Veeresha, P. and Prakasha, D. G. An efficient technique for two-dimensional fractional order biological population model, Int. J. Mod. Simul. Sci. Comput., (2050005), 1-17, (2020).
48. Mishra, B. K. and Keshri, N., Mathematical model on the transmission of worms in wireless sensor network, Appl. Math. Model., 37, 4103–4111, (2013).
49. Chunbo, L. and Chunfu, J., Modeling passive propagation of malwares on the WWW, Physics Procedia, 33, 271–278, (2012).
50. Yao, Y., Guo, L., Guo, H., Yu, G., Gao, F. X. and Tong, X. J., Pulse quarantine strategy of internet worm propagation: Modeling and analysis, Computers and Electrical Engineering, 38, 1047–1061, (2012).
51. Khayam, S. A. and Radha, H., Using signal processing techniques to model worm propagation over wireless sensor networks, IEEE Signal Processing Magazine, 164–169, (2006).
52. Wang, X. and Li, Y., An improved SIR model for analyzing the dynamics of worm propagation in wireless sensor networks, Chinese Journal of Electronics, 18, 8-12, (2009).
53. Wang, X., Li, Q. and Li, Y., EiSIRS: A formal model to analyze the dynamics of worm propagation in wireless sensor networks, J. Comb. Optim., 20, 47–62, (2010).
54. Wang, Y. and Yang, X., Virus spreading in wireless sensor networks with a medium access control mechanism, Chinese Phy. B, 22, 40200-40206, (2013).
55. Zhang, Z. and Si, F., Dynamics of a delayed SEIRS-V model on the transmission of worms in a wireless sensor network, Adv. Diff. Equ., 295, (2014).
56. Mittag-Leffler, G. M., Sur la nouvelle fonction E_α (x), C. R. Acad. Sci. Paris, 137, 554-558, (1903).
57. Loonker, D. and Banerji, P. K., Solution of fractional ordinary differential equations by natural transform, Int. J. Math. Eng. Sci., 12, (2), 1-7, (2013).