Existence, uniqueness, continuous dependence and Ulam stability of mild solutions for an iterative fractional differential equation

• Autores: Abderrahim Guerfi, Abdelouaheb Ardjouni
• Localización: Cubo: A Mathematical Journal, ISSN 0716-7776, ISSN-e 0719-0646, Vol. 24, Nº. 1, 2022, págs. 83-94
• Idioma: inglés
• DOI: 10.4067/S0719-06462022000100083
• Enlaces
  • Texto completo
• Resumen
  • español

    RESUMEN En este trabajo, estudiamos la existencia, unicidad, dependencia continua y estabilidad de Ulam de soluciones mild para una ecuación diferencial fraccionaria de Caputo iterativa, invirtiéndola primero como ecuación integral. Luego construimos una aplicación apropiada y empleamos el teorema del punto fijo de Schauder para demostrar nuestros nuevos resultados. Finalmente damos un ejemplo para ilustrar los resultados obtenidos.

  • English

    ABSTRACT In this work, we study the existence, uniqueness, continuous dependence and Ulam stability of mild solutions for an iterative Caputo fractional differential equation by first inverting it as an integral equation. Then we construct an appropriate mapping and employ the Schauder fixed point theorem to prove our new results. At the end we give an example to illustrate our obtained results.

• Referencias bibliográficas
  • Abbas, S.. (2011). Existence of solutions to fractional order ordinary and delay differential equations and applications. Electron. J. Differential...
  • Amer, A. A.,Darus, M.. (2012). An application of univalent solutions to fractional Volterra equation in complex plane. Transylv. J. Math....
  • Benchohra, M.,Henderson, J.,Ntouyas, S. K.,Ouahab, A.. (2008). Existence results for fractional order functional differential equations with...
  • Boulares, H.,Ardjouni, A.,Laskri, Y.. (2018). Existence and uniqueness of solutions to fractional order nonlinear neutral differential equations....
  • Cheraiet, S.,Bouakkaz, A.,Khemis, R.. (2021). Bounded positive solutions of an iterative threepoint boundary-value problem with integral boundary...
  • Diethelm, K.. (2003). Fractional differential equations, theory and numerical treatment. TU Braunschweig. Braunschweig.
  • El-Sayed, A. M. A.. (1995). Fractional order evolution equations. J. Fract. Calc.. 7. 89-100
  • Giannantoni, C.. (2003). The problem of the initial conditions and their physical meaning in linear differential equations of fractional order....
  • Hamoud, A. A.. (2021). Uniqueness and stability results for Caputo fractional Volterra-Fredholm integro-differential equations. Zh. Sib. Fed....
  • Kilbas, A. A.,Srivastava, H. M.,Trujillo, J. J.. (2006). Theory and applications of fractional differential equations. Elsevier Science B....
  • Machado, J. T.,Kiryakova, V.,Mainardi, F.. (2011). Recent history of fractional calculus. Commun. Nonlinear Sci. Numer. Simul.. 16. 1140
  • Miller, K. S.,Ross, B.. (1993). An introduction to the fractional calculus and fractional differential equations. John Wiley & Sons, Inc.....
  • Oldham, K. B.,Spanier, J.. (1974). The fractional calculus, Mathematics in Science and Engineering. Academic Press. New York-London.
  • Podlubny, I.. (1999). Fractional differential equations. Academic Press, Inc.. San Diego, CA.
  • Bhalekar, S.,Daftardar-Gejji, V.,Baleanu, D.,Magin, R.. (2012). Generalized fractional order Bloch equation with extended delay. Internat....
  • Samko, S. G.,Kilbas, A. A.,Marichev, O. I.. (1993). Fractional integrals and derivatives. Gordon and Breach Science Publishers. Yverdon.
  • Smart, D. R.. (1974). Fixed point theorems. Cambridge University Press. London-New York.
  • Wang, J.,Lv, L.,Zhou, Y.. (2011). Ulam stability and data dependence for fractional differential equations with Caputo derivative. Electron....
  • Zhao, H. Y.,Liu, J.. (2017). Periodic solutions of an iterative functional differential equation with variable coefficients. Math. Methods...