A new clique polynomial approach for fractional partial differential equations

References

[1] S. Kumbinarasaiah, “A new approach for the numerical solution for nonlinear Klein–Gordon equation,” SeMA, vol. 77, pp. 435–456, 2020. https://doi.org/10.1007/s40324-020-00225-y.Suche in Google Scholar

[2] S. Kumbinarasaiah, H. S. Ramane, K. Pise, and G. Hariharan, “Numerical-Solution-for-Nonlinear-Klein–Gordon equation via operational-matrix by clique polynomial of complete graphs,” Int. J. Appl. Comput. Math., vol. 7, p. 12, 2021. https://doi.org/10.1007/s40819-020-00943-x.Suche in Google Scholar

[3] S. Kumbinarasaiah and H. Rezazadeh, “Numerical solution for the fractional-order one-dimensional telegraph equation via wavelet technique,” Int. J. Nonlinear Sci. Numer. Stimul., vol. 22, no. 6, pp. 767–780, 2021. https://doi.org/10.1515/ijnsns-2019-0300.Suche in Google Scholar

[4] K. Srinivasa, H. Rezazadeh, and W. Adel, “Numerical investigation based on Laguerre wavelet for solving the hunter Saxton equation,” Int. J. Algorithm. Comput. Math., vol. 6, no. 5, pp. 1–14, 2020. https://doi.org/10.1007/s40819-020-00890-7.Suche in Google Scholar

[5] H. Tariq, H. Günerhan, H. Rezazadeh, and W. Adel, “A numerical approach for the nonlinear temporal conformable fractional foam drainage equation,” Asian Eur. J. Math., vol. 14, no. 6, p. 2150089, 2020. https://doi.org/10.1142/s1793557121500893.Suche in Google Scholar

[6] N. Ahmed, A. Elsonbaty, W. Adel, B. Dumitru, and M. Rafiq, “Stability analysis and numerical simulations of spatiotemporal HIV CD4+ T cell model with drug therapy,” Chaos, vol. 30, no. 8, p. 083122, 2020. https://doi.org/10.1063/5.0010541.Suche in Google Scholar PubMed

[7] R. A. Talarposhti, P. Jalili, H. Rezazadeh, B. Jalili, D. D. Ganji, W. Adel, and A. Bekir, “Optical soliton solutions to the (2 + 1)-dimensional Kundu–Mukherjee–Naskar equation,” Int. J. Mod. Phys. B, vol. 34, no. 11, p. 2050102, 2020. https://doi.org/10.1142/s0217979220501027.Suche in Google Scholar

[8] S. C. Shiralashetti and S. Kumbinarasaiah, “Hermite wavelets operational matrix of integration for the numerical solution of nonlinear singular initial value problems,” Alex. Eng. J., vol. 57, no. 4, pp. 2591–2600, 2018. https://doi.org/10.1016/j.aej.2017.07.014.Suche in Google Scholar

[9] S. C. Shiralashetti and S. Kumbinarasaiah, “Theoretical study on continuous polynomial wavelet bases through wavelet series collocation method for nonlinear lane-Emden type equations,” Appl. Math. Comput., vol. 315, pp. 591–602, 2017. https://doi.org/10.1016/j.amc.2017.07.071.Suche in Google Scholar

[10] A. A. Kilbas, H. M. Srivastava, and J. J. Trujillo, Theory and Applications of Fractional Differential Equations, vol. 204, Amesterdam, Elsevier, 2006.Suche in Google Scholar

[11] I. Podlubny, Fractional Differential Equations: An Introduction to Fractional Derivatives, Fractional Differential Equations, to Methods of Their Solution, and Some of Their Applications, USA, Elsevier, 1998.Suche in Google Scholar

[12] K. S. Miller and B. Ross, An Introduction to the Fractional Calculus and Fractional Differential Equations, Canada, Wiley, 1993.Suche in Google Scholar

[13] I. Podlubny, Fractional Derivative Equations, San Diego, Academic Press, 1999.Suche in Google Scholar

[14] A. Saadatmandi and M. Dehghan, “A new operational matrix for solving fractional-order differential equations,” Comput. Math. Appl., vol. 59, pp. 1326–1336, 2010. https://doi.org/10.1016/j.camwa.2009.07.006.Suche in Google Scholar

[15] S. alfaqeih and E. Misirli, “Conformable double Laplace transform method for solving conformable fractional partial differential equations,” Comput. Methods Differ. Equ., vol. 9, no. 3, pp. 908–918, 2021. https://doi.org/10.22034/cmde.2020.38135.1678.Suche in Google Scholar

[16] A. Atangana, “On the new fractional derivative and application to nonlinear Fisher’s reaction diffusion equation,” Appl. Math. Comput., vol. 273, pp. 948–956, 2016. https://doi.org/10.1016/j.amc.2015.10.021.Suche in Google Scholar

[17] Atangana, A., and Baleanu, D. “New fractional derivatives with nonlocal and non-singular kernel: theory and application to heat transfer model,” 2016. arXiv preprint arXiv:1602.03408.10.2298/TSCI160111018ASuche in Google Scholar

[18] R. Agarwal, M. Belmekki, and M. Benchohra, “A survey on semilinear differential equations and inclusions involving Riemann-Liouville fractional derivative,” Adv. Differ. Equ., vol. 2009, pp. 1–47, 2009. https://doi.org/10.1155/2009/981728.Suche in Google Scholar

[19] R. Khalil, M. Al Horani, A. Yousef, and M. Sababheh, “A new definition of fractional derivative,” J. Comput. Appl. Math., vol. 264, pp. 65–70, 2014. https://doi.org/10.1016/j.cam.2014.01.002.Suche in Google Scholar

[20] Y. Sun and W. Sumelka, “Fractional viscoplastic model for soils under compression,” Acta Mech., vol. 230, no. 9, pp. 3365–3377, 2019. https://doi.org/10.1007/s00707-019-02466-z.Suche in Google Scholar

[21] R. A. Z. Daou, F. E. Samarani, C. Yaacoub, and X. Moreau, “Fractional derivatives for edge detection: application to road obstacles,” in Smart Cities Performability, Cognition, Security, Springer, Cham, Springer International Publishing, 2019, pp. 115–137.10.1007/978-3-030-14718-1_6Suche in Google Scholar

[22] Y. Zhang, H. Sun, H. H. Stowell, M. Zayernouri, and S. E. Hansen, “A review of applications of fractional calculus in earth system dynamics,” Chaos Solit. Fractals, vol. 102, p. 2946, 2017. https://doi.org/10.1016/j.chaos.2017.03.051.Suche in Google Scholar

[23] R. M. Evans, U. N. Katugampola, and D. A. Edwards, “Applications of fractional calculus in solving abel-type integral equations: surface, volume reaction problem,” Comput. Math. Appl., vol. 73, no. 6, pp. 1346–1362, 2017. https://doi.org/10.1016/j.camwa.2016.12.005.Suche in Google Scholar

[24] N. Engheia, “On the role of fractional calculus in electromagnetic theory,” IEEE Antenn. Propag. Mag., vol. 39, no. 4, pp. 35–46, 1997. https://doi.org/10.1109/74.632994.Suche in Google Scholar

[25] M. A. Matlob and Y. Jamali, “The concepts and applications of fractional order differential calculus in modeling of viscoelastic systems: a primer,” Crit. Rev. Biomed. Eng., vol. 47, no. 4, pp. 249–276, 2019. https://doi.org/10.1615/CritRevBiomedEng.2018028368.Suche in Google Scholar PubMed

[26] S. Aman, I. Khan, Z. Ismail, and M. Z. Salleh, “Applications of fractional derivatives to nanofluids: exact and numerical solutions,” Math. Model Nat. Phenom., vol. 13, no. 1, p. 2, 2018. https://doi.org/10.1051/mmnp/2018013.Suche in Google Scholar

[27] X. J. Yang, J. T. Machado, C. Cattani, and F. Gao, “On a fractal LC-electric circuit modeled by local fractional calculus,” Commun. Nonlinear Sci. Numer. Simulat., vol. 47, pp. 200–206, 2017. https://doi.org/10.1016/j.cnsns.2016.11.017.Suche in Google Scholar

[28] D. Bleanu and A. M. Lopes, Eds., Applications in Engineering, Life and Social Sciences, Berlin, Walter de Gruyter GmbH Co KG, 2019.Suche in Google Scholar

[29] R. Hilfer, Ed. Applications Of Fractional Calculus in Physics, vol 35, Singapore, World scientific, 2000, pp. 87–130.10.1142/9789812817747_0002Suche in Google Scholar

[30] Z. U. A. Zafar, N. Sene, H. Rezazadeh, and N. Esfandian, “Tangent nonlinear equation in context of fractal fractional operators with nonsingular kernel,” Math. Sci., pp. 1–11, 2021. https://doi.org/10.1007/s40096-021-00403-7.Suche in Google Scholar PubMed PubMed Central

[31] R. M. Jena, S. Chakraverty, H. Rezazadeh, and D. Domiri Ganji, “On the solution of time‐fractional dynamical model of Brusselator reaction‐diffusion system arising in chemical reactions,” Math. Methods Appl. Sci., vol. 43, no. 7, pp. 3903–3913, 2020. https://doi.org/10.1002/mma.6141.Suche in Google Scholar

[32] Z. U. A. Zafar, H. Rezazadeh, M. Inc, K. S. Nisar, T. A. Sulaiman, and A. Yusuf, “Fractional order heroin epidemic dynamics,” Alex. Eng. J., vol. 60, no. 6, pp. 5157–5165, 2021. https://doi.org/10.1016/j.aej.2021.04.039.Suche in Google Scholar

[33] A. Dabiri, E. A. Butcher, and M. Nazari, “Coefficient of restitution in fractional viscoelastic compliant impacts using fractional Chebyshev collocation,” J. Sound Vib., vol. 388, pp. 230–244, 2017. https://doi.org/10.1016/j.jsv.2016.10.013.Suche in Google Scholar

[34] M. A. Bayrak, A. Demir, and E. Ozbilge, “On the numerical solution of conformable fractional diffusion problem with small delay,” Numer. Methods Part. Differ. Equ., pp. 1–13, 2020. https://doi.org/10.1002/num.22640.Suche in Google Scholar

[35] K. M. Saad, M. M. Khader, J. F. Gmez-Aguilar, and D. Baleanu, “Numerical solutions of the fractional Fishers type equations with Atangana-Baleanu fractional derivative by using spectral collocation methods,” Chaos, vol. 29, no. 2, p. 023116, 2019. https://doi.org/10.1063/1.5086771.Suche in Google Scholar PubMed

[36] C. Hoede and X. Li, “Clique polynomials and independent set polynomials of graphs,” Discrete Math., vol. 125, pp. 219–228, 1994. https://doi.org/10.1016/0012-365x(94)90163-5.Suche in Google Scholar

[37] F. Harary, Graph Theory, Reading, Addison-Wesley, 1969.10.21236/AD0705364Suche in Google Scholar

[38] Q. Wu, “The maximum clique problems with applications to graph coloring,” Doctoral Dissertation, Université d’Angers, 2013.Suche in Google Scholar

[39] E. J. Farrell, “An introduction to matching polynomials,” J. Combin. Theor. B, vol. 27, no. 1, pp. 75–86, 1979. https://doi.org/10.1016/0095-8956(79)90070-4.Suche in Google Scholar

[40] N. H. Tuan, R. M. Ganji, and H. Jafari, “A numerical study of fractional rheological models and fractional Newell-Whitehead-Segel equation with non-local and non-singular kernel,” Chin. J. Phys., vol. 68, pp. 308–320, 2020. https://doi.org/10.1016/j.cjph.2020.08.019.Suche in Google Scholar

[41] R. M. Ganji, H. Jafari, and S. Nemati, “A new approach for solving integro-differential equations of variable order,” J. Comput. Appl. Math., vol. 379, p. 112946, 2020. https://doi.org/10.1016/j.cam.2020.112946.Suche in Google Scholar