Existence and attractivity results for ѱ-Hilfer hybrid fractional differential equations

• Autores: Fatima Si Bachir, Saïd Abbas, Maamar Benbachir, Mouffak Benchohra, Gaston Mandata N'Guérékata
• Localización: Cubo: A Mathematical Journal, ISSN 0716-7776, ISSN-e 0719-0646, Vol. 23, Nº. 1, 2021, págs. 145-159
• Idioma: inglés
• DOI: 10.4067/S0719-06462021000100145
• Enlaces
  • Texto completo
• Resumen
  • español

    Resumen En este trabajo, presentamos algunos resultados sobre la existencia de soluciones atractivas de ecuaciones diferenciales fraccionarias de tipo ѱ-Hilfer híbridas. Los resultados de existencia de soluciones son consecuencia del teorema de punto fijo de Schauder. A continuación, probamos que todas las soluciones son uniformemente localmente atractivas.

  • English

    Abstract In this work, we present some results on the existence of attractive solutions of fractional differential equations of the ѱ-Hilfer hybrid type. The results on the existence of solutions are a consequence of the Schauder fixed point theorem. Next, we prove that all solutions are uniformly locally attractive.

• Referencias bibliográficas
  • Abbas, S.,Benchohra, M.. (2015). Advanced Functional Evolution Equations and Inclusions. Springer. Cham.
  • Abbas, S.,Benchohra, M.. (2013). Existence and stability of nonlinear fractional order RiemannLiouville, Volterra-Stieltjes multi-delay integral...
  • Abbas, S.,Benchohra, M.,Diagana, T.. (2013). Existence and attractivity results for some fractional order partial integrodifferential equations...
  • Abbas, S.,Benchohra, M.,Henderson, J.. (2019). Existence and attractivity results for Hilfer fractional differential equations. J. Math. Sci.....
  • Abbas, S.,Benchohra, M.,N’Guérékata, G. M.. (2015). Advanced Fractional Differential and Integral Equations. Nova Sci. Publ.. New York.
  • Abbas, S.,Benchohra, M.,Guérékata, G. M.N’. (2015). Topics in Fractional Differential Equations. Springer. New York.
  • Abbas, S.,Benchohra, M.,Nieto, J. J.. (2012). Global attractivity of solutions for nonlinear fractional order Riemann-Liouville Volterra-Stieltjes...
  • Almeida, R.. (2020). Functional differential equations involving the (psi)-Caputo fractional derivative. Fractal and Fractional. 4. 1-8
  • Ahmad, B.,Ntouyas, S. K.,Tariboon, J.. (2016). A nonlocal hybrid boundry value problem of Caputo fractional integro-differential equations....
  • Almeida, R.. (2017). A Caputo, fractional derivative of a function with respect to another function. Comm. Nonlinear Sci. Numer. Simulat.....
  • Corduneanu, C.. (1973). Integral Equations and Stability of Feedback Systems. Acad. Press. New York.
  • Dhage, B. C.,Lakshmikantham, V.. (2010). Basic results on hybrid differential equations. Nonlinear Anal.: Hybrid Systems. 4. 414
  • Diethelm, K.. (2010). The analysis of fractional differential equations, Lecture Notes in Mathematics. Springer-verlag. Berlin Heidelberg.
  • Ferraoun, S.,Dahmani, Z.. (2020). Existence and stability of solutions of a class of hybrid fractional differential equations involving R-L-operator....
  • Granas, A.,Dugundji, J.. (2003). Fixed Point Theory. Springer-Verlag. New York.
  • Kharade, J. P.,Kucche, K. D.. (2019). On the impulsive implicit -Hilfer fractional differential equations with delay. Math. Methods Appl....
  • Kilbas, A. A.,Srivastava, H. M.,Trujillo, J. J.. (2006). Theory and Applications of Fractional Differential Equations. Elsevier. Amsterdam.
  • Kucche, K. D.,Mali, A. D.,Sousa, J. V.. (2019). On the nonlinear Ψ-Hilfer fractional differential equations. Comput. Appl. Math.. 38. 25
  • Lakshmikantham, V.,Vasundhara Devi, J.. (2008). Theory of fractional differential equations in a Banach space. Eur. J. Pure Appl. Math.. 1....
  • Lakshmikantham, V.,Vatsala, A. S.. (2008). Basic theory of fractional differential equations. Nonlin. Anal.. 69. 2677
  • Lakshmikantham, V.,Vatsala, A. S.. (2008). General uniqueness and monotone iterative technique for fractional differential equations. Appl....
  • Oldham, K.,Spanier, J.. (1974). The Fractional Calculus. Academic Press. New York.
  • Podlubny, I.. (1999). Fractional Differential Equations. Acad. Press.
  • Samko, S. G.,Kilbas, A. A.,Marichev, O. I.. (1993). Fractional Integrals and Derivatives: Theory and Applications. Gordon Breach. Tokyo-Paris-Berlin....
  • Sugumarana, H.,Ibrahimb, R. W.,Kanagarajana, K.. (2018). On Ψ-Hilfer fractional differential equation with complex order. Universal J. Math....
  • Sun, S.,Zhao, Y.,Han, Z.,Li, Y.. (2012). The existence of solutions for boundary value problem of fractional hybrid differential equations....
  • Tarasov, V. E.. (2010). Fractional Dynamics: Application of Fractional Calculus to the Dynamics of Particles, Fields, and Media. Springer....
  • C. Sousa, J. Vanterler da,Tenreiro Machado, J. A.,Capelas de Oliveira, E.. (2020). The Ψ-Hilfer fractional calculus of variable order and...
  • C. Sousa, J. Vanterler da,Capelas de Oliveira, E.. (2018). On the -Hilfer fractional derivative. Commun. Nonlinear Sci. Numer. Simulat.. 60....
  • C. Sousa, J. Vanterler da,Capelas de Oliveira, E.. (2019). On the -fractional integral and applications. Comput. Appl. Math.. 38. 1-22
  • Zhao, Y.,Sun, S.,Han, Z.,Li, Q.. (2011). Theory of fractional hybrid differential equations. Comput. Math. Appl.. 62. 1312
  • Zhou, Y.. (2014). Basic Theory of Fractional Differential Equations. World Scientific. Singapore.
  • Zhou, Y.. (2016). Fractional Evolution Equations and Inclusions: Analysis and Control. Elsevier, Acad. Press.
  • Zhou, Y.,Wang, J.,Zhang, L.. (2017). Basic Theory of Fractional Differential Equations. World Scientific. Singapore.