Bounded Non-oscillatory Solutions of Nabla Forced Fractional Difference Equations with Positive and Negative Terms

• Autores: J. Alzabut, Said R. Grace, Jagan Mohan Jonnalagadda, Ethiraju Thandapani
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 22, Nº 1, 2023
• Idioma: inglés
• Enlaces
  • Texto completo
• Resumen

  • This paper studies the boundedness of non-oscillatory solutions of nabla fractional difference equations with positive and negative terms. Unlike the methods existing in the literature, our approach is primarily based on the new defined properties of discrete fractional calculus and some mathematical inequalities. Examples are provided to support the validity of the obtained results.

• Referencias bibliográficas
  • 1. Abdalla, B., Abodayeh, K., Abdeljawad, T., Alzabut, J.: New oscillation criteria for forced nonlinear fractional difference equations....
  • 2. Abdalla, B., Alzabut, J., Abdeljawad, T.: On the oscillation of higher order fractional difference equations with mixed nonlinearities....
  • 3. Alzabut, J., Abdeljawad, T., Alrabaiah, H.: Oscillation criteria for forced and damped nabla fractional difference equations. J. Comput....
  • 4. Alzabut, J.O., Abdeljawad, T.: Sufficient conditions for the oscillation of nonlinear fractional difference equations. J. Fract. Calc....
  • 5. Alzabut, J., Muthulakshmi, V., Özbekler, A., Adıgüzel, H.: On the oscillation of non-linear fractional difference equations with damping....
  • 6. Anastassiou, G.A.: Nabla discrete fractional calculus and nabla inequalities. Math. Comput. Model. 51, 562 (2010)
  • 7. Atıcı F.M., Eloe P.W.: Discrete fractional calculus with the nabla operator. Electron. J. Qual. Theory Differ. Equ. Special Edition I,...
  • 8. Chen, F.: Fixed points and asymptotic stability of nonlinear fractional difference equations. Electron. J. Qual. Theory Differ. Equ. 39,...
  • 9. Goodrich, C., Peterson, A.C.: Discrete Fractional Calculus. Springer, Cham (2015)
  • 10. Grace, S.R., Graef, J.R., Tunc, E.: On the boundedness of non-oscillatory solutions of certain fractional differential equations with...
  • 11. Hardy, G.H., Littlewood, J.E., Polya, G.: Inequalities, Reprint of the 1952 Edition. Cambridge University Press, Cambridge (1988)
  • 12. Harikrishnan, S., Kanagarajan, K., Elsayed, E.M.: Existence and stability results for differential equations with complex order involving...
  • 13. Jonnalagadda, J.M.: Analysis of a system of nonlinear fractional nabla difference equations. Int. J. Dyn. Syst. Differ. Equ. 5, 149 (2015)
  • 14. Kelley, W.G., Peterson, A.C.: Difference Equations. Harcourt/Academic Press, San Diego (2001)
  • 15. Kilbas, A.A., Srivastava, H.M., Trujillo, J.J.: Theory and Applications of Fractional Differential Equations, North-Holland Mathematics...
  • 16. Podlubny, I.: Fractional Differential Equations. Academic Press Inc., San Diego (1999)
  • 17. Vivek, D., Kanagarajan, K., Elsayed, E.M.: Some existence and stability results for Hilfer-fractional implicit differential equations...