Picone Identities of a Certain Class of Conformable Half Linear Anisotropic Biharmonic Equations
DOI:
https://doi.org/10.11113/mjfas.v21n1.3549Keywords:
Picone identities, anisotropic biharmonic equations, anisotropic hardy type inequality, oscillation.Abstract
Main aim of this article, we derive sufficient conditions of new results for Picone identities for a certain class of conformable half-linear anisotropic biharmonic equations. We derive a Strumiancomparison theorem and oscillation results. Furthermore, the oscillation results are different from the most known ones in the sense that they are based on the information for radial solutions. This paper's expand upon and broaden a few of the previously established results for conformable half-linear anisotropic biharmonic equations. If and then conformable half-linear anisotropic biharmonic equations (4) become the classical biharmonic equation. These novel outcomes add to the body of knowledge already available in the classical example. To illustrate the usefulness of our new results, we give an example.
References
Abdelijawad, T. (2015). On conformable fractional calculus. Journal of Computational and Applied Mathematics, 279, 57–66.
Agarwal, R. P., Grace, S. R., & Regan, D. O. (2000). Oscillation theory for difference and functional differential equations. Marcel Dekker, Kluwer Academic, Dordrecht.
Agarwal, R. P., & Regan, D. O. (2008). An introduction to ordinary differential equations. Springer, New York.
Antontsev, S. N., Diaz, J. I., & Shmarev, S. (2012). Energy methods for free boundary problems: Applications to nonlinear PDEs and fluid mechanics. Springer, Berlin.
Atangana, A., Baleanu, D., & Alsaedi, A. (2015). New properties of conformable derivatives. Open Mathematics, 7(2), 889–898.
Bear, J. (1972). Dynamics of fluids in porous media. Elsevier, New York.
Feng, T. E., & Cui, X. (2017). Anisotropic Picone identities and anisotropic Hardy inequalities. Journal of Inequalities and Applications, 16.
Hilfer, H. (2000). Applications of fractional calculus in physics. World Scientific Publishing Company, Singapore.
Khalil, R. R., Horani, A. M., Yousef, A., & Sababheh, M. (2014). A new definition of fractional derivative. J. Com. Appl. Math., 264, 65–70.
Kilbas, A. A., Srivastava, H. M., & Trujillo, J. J. (2006). Theory and applications of fractional differential equations. Elsevier Science B.V., Amsterdam, The Netherlands.
Kilicman, A., Sadhasivam, V., Deepa, M., & Nagajothi, N. (2018). Oscillatory behavior of three-dimensional α-fractional delay differential equations. Symmetry, 10(12), 769.
Kreith, K. (1969). A comparison theorem for fourth-order differential equations. Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur., 46, 664–666.
Kreith, K. (1972). A Picone identity for fourth-order differential equations. Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur., 52, 455–456.
Lions, J. (1969). Quelques methods de resolution des problems aux limites non lineaires. Dunod, Paris.
Priyadharshini, S., & Sadhasivam, V. (2022). Forced oscillation of solutions of conformable hybrid elliptic partial differential equations. Journal of Computational Mathematica, 6(1), 396–412.
Santra, S. S., Priyadharshini, S., Sadhasivam, V., Kavitha, J., Fernandez-Gamiz, U., Noeiaghdam, S., & Khedher, K. M. (2023). On the oscillation of certain classes of conformable Emden-Fowler type elliptic partial differential equations. AIMS Mathematics, 8(6), 12622–12636.
Sasikala, N., & Sadhasivam, V. (2024). Anisotropic Picone identities for half-linear conformable elliptic equations. Journal of Mechanics of Continua and Mathematical Sciences, 19(6), 55–66.
Swanson, C. (1968). Comparison and oscillation theory of linear differential equations. Academic Press, New York.
Tanigawa, T., & Yoshida, N. (2004). Picone identities for ordinary differential equations of fourth order. Math. J. Toyama Univ., 27, 91–99.
Tyagi, J. (2013). A nonlinear Picone’s identity and its applications. Appl. Math. Lett., 26(6), 624–626.
Weickert, J. (1998). Anisotropic diffusion in image processing. Teubner, Stuttgart.
Yoshida, N. (2008). Oscillation theory of partial differential equations. World Scientific, Singapore.
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