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On a Coupled Impulsive Fractional Integrodifferential System with Hadamard Derivatives

  • Alam, Mehboob [1] ; Zada, Akbar [1] ; Riaz, Usman [1]
    1. [1] University of Peshawar

      University of Peshawar

      Pakistán

  • Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 21, Nº 1, 2022
  • Idioma: inglés
  • Enlaces
  • Resumen

    • The main intention of the present research study is focused on the analysis of coupled impulsive fractional integrodifferential system having Hadamard derivatives. With the help of fixed point theorem attributed to Krasnoselskii’s, we investigate desired existence and uniqueness results. Moreover, we present different kinds of stability such as Hyers–Ulam stability, generalized Hyers–Ulam stability, Hyers–Ulam–Rassias stability, and generalized Hyers–Ulam–Rassias stability using the classical technique of functional analysis. Next, an example is designed to examine our findings based on the procedures applied in the theorems.

  • Referencias bibliográficas
    • 1. Abdo, M.S., Abdeljawad, T., Shah, K., Jarad, F.: Study of impulsive problems under Mittag–Leffler power law. Heliyon 6, e05109 (2020)
    • 2. Ahmad, M., Zada, A., Alzabut, J.: Hyers–Ulam stability of a coupled system of fractional differential equations of Hilfer–Hadamard type....
    • 3. Alam, M., Shah, D.: Hyers–Ulam stability of coupled implicit fractional integro-differential equations with Riemann–Liouville derivatives....
    • 4. Alam, M., Zada, A., Popa, I.L., et al.: A fractional differential equation with multi-point strip boundary condition involving the Caputo...
    • 5. Ali, Z., Zada, A., Shah, K.: Ulam stability to a toppled systems of nonlinear implicit fractional order boundary value problem. Bound....
    • 6. Altman, M.: A fixed point theorem for completely continuous operators in Banach spaces. Bull. Acad. Pol. Sci. 3, 409–413 (1955)
    • 7. Andronov, A., Witt, A., Haykin, S.: Oscilation Theory. Nauka, Moskow (1981)
    • 8. Babitskii, V., Krupenin, V.: Vibration in Strongly Nonlinear Systems. Nauka, Moskow (1985)
    • 9. Babusci, D., Dattoli, G., Sacchetti, D.: The Lamb–Bateman integral equation and the fractional derivatives. Fract. Calc. Appl. Anal. 14(2),...
    • 10. Bainov, D., Dimitrova, M., Dishliev, A.: Oscillation of the bounded solutions of impulsive differential–difference equations of second...
    • 11. Benchohra, M., Lazreg, J.E.: Existence and Ulam stability for nonlinear implicit fractional differential equations with Hadamard derivative....
    • 12. Chernousko, F., Akulenko, L., Sokolov, B.: Control of Oscillations. Nauka, Moskow (1980)
    • 13. Chua, L., Yang, L.: Cellular neural networks: applications. IEEE Trans Circuits Syst. CAS 1988(35), 1273–1290 (1988)
    • 14. Garra, R., Polito, F.: On some operators involving Hadamard derivatives. Integr. Transf. Spec. Funct. 24(10), 773–782 (2013)
    • 15. Hadamard, J.: Essai sur l’étude des fonctions, données par leur développement de Taylor. GauthierVillars (1892)
    • 16. Hao, X., Sun, H., Liu, L., Wang, D.: Positive solutions for semipositone fractional integral boundary value problem on the half-line....
    • 17. Jiang, J., O’Regan, D., Xu, J., Fu, Z.: Positive solutions for a system of nonlinear Hadamard fractional differential equations involving...
    • 18. Jung, S.M.: Hyers–Ulam stability of linear differential equations of first order. Appl. Math. Lett. 19, 854–858 (2006)
    • 19. Kilbas, A.A., Srivastava, H.M., Trujillo, J.J.: Theory and Application of Fractional Differential Equation. North-Holland and Mathematics...
    • 20. Lakshmikanthan, V., Bainov, D.D., Simeonov, P.S.: Theory of Impulsive Differential Equations. World Scientific, Singapore (1989)
    • 21. Luo, D., Alam, M., Zada, A., Riaz, U., Luo, Z.: Existence and stability of implicit fractional differential equations with Stieltjes boundary...
    • 22. Obloza, M.: Hyers stability of the linear differential equation. Rocznik NaukDydakt Prace Mat. 13, 259–270 (1993)
    • 23. Oldham, K.B.: Fractional differential equations in electrochemistry. Adv. Eng. Softw. 41, 9–12 (2010)
    • 24. Popov, E.: The Dynamics of Automatic Control Systems. Gostehizdat, Moskow (1964)
    • 25. Riaz, U., Zada, A., Ali, Z., et al.: Analysis of nonlinear coupled systems of impulsive fractional differential equations with Hadamard...
    • 26. Riaz, U., Zada, A., Ali, Z., et al.: On a Riemann–Liouville type implicit coupled system via generalized boundary conditions. Mathematics...
    • 27. Riaz, U., Zada, A., Ali, Z., Cui, Y., Xu, J.: Analysis of coupled systems of implicit impulsive fractional differential equations involving...
    • 28. Rihan, F.A.: Numerical modeling of fractional order biological systems. Abs. Appl. Anal. 2013, 816803 (2013). https://doi.org/10.1155/2013/816803
    • 29. Rizwan, R., Zada, A., Wang, X.: Stability analysis of non linear implicit fractional Langevin equation with noninstantaneous impulses....
    • 30. Rus, I.A.: Ulam stabilities of ordinary differential equations in a Banach space. Carpath. J. Math. 26, 103–107 (2010)
    • 31. Sabatier, J., Agrawal, O.P., Machado, J.A.T.: Advances in Fractional Calculus. Springer, Dordrecht (2007)
    • 32. Samko, S.G., Kilbas, A.A., Marichev, O.I.: Fractional Integrals and Derivatives: Theory and Applications. Gordon and Breach, Yverdon (1993)
    • 33. Shah, K., Ali, A., Bushnaq, S.: Hyers–Ulam stability analysis to implicit Cauchy problem of fractional differential equations with impulsive...
    • 34. Shah, K., Khalil, H., Khan, R.A.: Investigation of positive solution to a coupled system of impulsive boundary value problems for nonlinear...
    • 35. Subramanian, M., Alzabut, J., Baleanu, D., et al.: Existence, uniqueness and stability analysis of a coupled fractional-order differential...
    • 36. Tarasov, V.E.: Fractional Dynamics: Application of Fractional Calculus to Dynamics of Particles, Fields and Media. Springer, Heidelberg...
    • 37. Ulam, S.M.: A Collection of the Mathematical Problems. Interscience, New York (1960)
    • 38. Wang, X., Alam, M., Zada, A.: On coupled impulsive fractional integro-differential equations with Riemann–Liouville derivatives. AIMS...
    • 39. Wang, G., Pei, K., Chen, Y.: Stability analysis of nonlinear Hadamard fractional differential system. J. Frankl. Inst. 356(12), 6538–6546...
    • 40. Wang, J., Shah, K., Ali, A.: Existence and Hyers–Ulam stability of fractional nonlinear impulsive switched coupled evolution equations....
    • 41. Xu, J., Goodrich, C.S., Cui, Y.: Positive solutions for a system of first-order discrete fractional boundary value problems with semipositone...
    • 42. Zada, A., Alam, M., Riaz, U.: Analysis of q-fractional implicit boundary value problem having Stieltjes integral conditions. Math. Methods...
    • 43. Zada, A., Ali, W., Park, C.: Ulam’s type stability of higher order nonlinear delay differential equations via integral inequality of Grönwall–Bellman–Bihari’s...
    • 44. Zada, A., Alzabut, J., Waheed, H., Popa, I.L.: Ulam–Hyers stability of impulsive integrodifferential equations with Riemann–Liouville...
    • 45. Zada, A., Riaz, U., Khan, F.: Hyers–Ulam stability of impulsive integral equations. Boll. Unione Mat. Ital. 12(3), 453–467 (2019)
    • 46. Zavalishchin, S., Sesekin, A.: Impulsive Processes: Models and Applications. Nauka, Moskow (1991)
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