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Generalized Fractional Differential Systems with Stieltjes Boundary Conditions

  • Nemat Nyamoradi [1] ; Bashir Ahmad [2]
    1. [1] Razi University

      Razi University

      Irán

    2. [2] King Abdulaziz University

      King Abdulaziz University

      Arabia Saudí

  • Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 22, Nº 1, 2023
  • Idioma: inglés
  • Enlaces
  • Resumen

    • In this work, we study the existence of solutions to a new class of boundary value problems consisting of a system of nonlinear differential equations with generalized fractional derivative operators of different orders and nonlocal boundary conditions containing Riemann-Stieltjes and generalized fractional integral operators. We emphasize that the nonlinearities in the given system are of general form as they depend on the unknown functions as well as their lower order generalized fractional derivatives. The uniqueness result for the given problem is proved by applying the Banach contraction mapping principle, while the existence of solutions for the given system is shown with the aid of Leray-Schauder alternative. Two concrete examples are given for illustrating the obtained results. The paper concludes with some interesting observations.

  • Referencias bibliográficas
    • 1. Abbas, M.I., Feˇckan, M.: Michal Feckan, Investigation of an implicit Hadamard fractional differential equation with Riemann-Stieltjes...
    • 2. Ahmad, B., Alghanmi, M., Ntouyas, S.K., Alsaedi, A.: Fractional differential equations involving generalized derivative with Stieltjes...
    • 3. Ahmad, B., Ntouyas, S.K.: Existence results for a coupled system of Caputo type sequential fractional differential equations with nonlocal...
    • 4. Ahmad, B., Ntouyas, S., Alsaedi, A.: On a coupled system of fractional differential equations with coupled nonlocal and integral boundary...
    • 5. Ahmad, B., Luca, R.: Existence of solutions for a system of fractional differential equations with coupled nonlocal boundary conditions....
    • 6. Ahmad, B., Alghanmi, M., Alsaedi, A.: Existence results for a nonlinear coupled system involving both Caputo and Riemann-Liouville generalized...
    • 7. Alruwaily, Y., Ahmad, B., Ntouyas, S.K., Alzaidi, A.S.M.: Existence Results for Coupled Nonlinear Sequential Fractional Differential Equations...
    • 8. Arena, P., Caponetto, R., Fortuna, L., Porto, D.: Chaos in a fractional order Duffing system, In:Proceedings of the 1997 European conference...
    • 9. Asawasamrit, S., Thadang, Y., Ntouyas, S.K., Tariboon, J.: Non-Instantaneous Impulsive Boundary Value Problems Containing Caputo Fractional...
    • 10. Belmor, S., Ravichandran, C., Jarad, F.: Nonlinear generalized fractional differential equations with generalized fractional integral...
    • 11. Belmor, S., Jarad, F., Abdeljawad, T., Kilinç, G.: A study of boundary value problem for generalized fractional differential in- clusion...
    • 12. Belmor, S., Jarad, F., Abdeljawad, T.: On Caputo-, Hadamard type coupled systems of nonconvex fractional differential inclusions. Adv....
    • 13. Belmor, S., Jarad, F., Abdeljawad, T., Alqudah, M.A.: On fractional differential inclusion problems involving fractional order derivative...
    • 14. Faieghi, M., Kuntanapreeda, S., Delavari, H., Baleanu, D.: LMI-based stabilization of a class of fractional-order chaotic systems. Nonlinear...
    • 15. Ge, Z.M., Jhuang, W.R.: Chaos, control and synchronization of a fractional order rotational mechanical system with a centrifugal governor....
    • 16. Ge, Z.M., Ou, C.Y.: Chaos synchronization of fractional order modified Duffing systems with parameters excited by a chaotic signal. Chaos...
    • 17. Granas, A., Dugundji, J.: Fixed Point Theory. Springer-Verlag, New York (2003)
    • 18. Grigorenko, I., Grigorenko, E.: Chaotic dynamics of the fractional Lorenz system. Phys. Rev. Lett. 91, 034101 (2003)
    • 19. Hartley, T.T., Lorenzo, C.F., Killory, Q.H.: Chaos in a fractional order Chua’s system. IEEE Trans. CAS-I 42, 485–490 (1995)
    • 20. Henderson, J., Luca, R., Tudorache, A.: On a system of fractional differential equations with coupled integral boundary conditions. Fract....
    • 21. Hilfer, R. (ed.): Applications of Fractional Calculus in Physics. World Scientific, Singapore (2000)
    • 22. Jiang, J., Liu, L., Wu, Y.: Positive solutions to singular fractional differential system with coupled boundary conditions. Comm. Nonlinear...
    • 23. Jiao, Z., Chen, Y.Q., Podlubny, I.: Distributed-order Dyn. Syst. Springer, New York (2012)
    • 24. Katugampola, U.N.: New approach to a generalized fractional integral. Appl. Math. Comput. 218, 860–865 (2015)
    • 25. Katugampola, U.N.: A new approach to generalized fractional derivatives. Bull. Math. Anal. Appl. 6, 1–15 (2014)
    • 26. Kilbas, A.A., Trujillo, J.J.: Differential equations of fractional order: Methods, results and problems I. Appl. Anal. 78, 153–192 (2001)
    • 27. Kilbas, A.A., Trujillo, J.J.: Differential equations of fractional order: Methods, results and problems II. Appl. Anal. 81, 435–493 (2002)
    • 28. Kusnezov, D., Bulgac, A., Dang, G.D.: Quantum Levy processes and fractional kinetics. Phys. Rev. Lett. 82, 1136–11399 (1999)
    • 29. Lu, H., Sun, S., Yang, D., Teng, H.: Theory of fractional hybrid differential equations with linear perturbations of second type. Bound....
    • 30. Lupinska, B., Odzijewicz, T.: A Lyapunov-type inequality with the Katugampola fractional derivative. Math. Methods Appl. Sci. 41, 8985–8996...
    • 31. Metzler, R., Klafter, J.: The random walks guide to anomalous diffusion: a fractional dynamics approach. Phys. Rep. 339, 1–77 (2000)
    • 32. Ostoja-Starzewski, M.: Towards thermoelasticity of fractal media. J. Therm. Stress 30, 889–896 (2007)
    • 33. Povstenko, Y.Z.: Fract thermoelast. Springer, New York (2015)
    • 34. Redhwan, S.S., Shaikh, S.L., Abdo, M.S.: Implicit fractional differential equation with anti-periodic boundary condition involving Caputo-Katugampola...
    • 35. Redhwan, S.S., Shaikh, S.L., Abdo, M.S., Shatanawi, W., Abodayeh, K., Almalahi, M.A., Aljaaidi, T.: Investigating a generalized Hilfer-type...
    • 36. S.S. Redhwan, S.L. Shaikh, M.S. Abdo, Theory of Nonlinear Caputo-Katugampola Fractional Differential Equations, arXiv:1911.08884 13 (2019)
    • 37. Redhwan, S.S., Shaikh, S.L., Abdo, M.S.: Caputo-Katugampola type implicit fractional differential equation with two-point anti-periodic...
    • 38. Sokolov, I.M., Klafter, J., Blumen, A.: Fractional kinetics. Phys. Today. 55, 48–54 (2002)
    • 39. Su, X.: Boundary value problem for a coupled system of nonlinear fractional differential equations. Appl. Math. Lett. 22, 64–69 (2009)
    • 40. Sabatier, J., Agarwal, O.P., Ttenreiro Machado, J.A.: Advances in Fractional Calculus. Theoretical Developments and Applications in Physics...
    • 41. Ttenreiro Machado, J.A.: Discrete time fractional-order controllers. Frac. Cal. App. Anal. 4, 47–66 (2001)
    • 42. Waheed, H., Zada, A., Rizwan, R., Popa, I.L.: Hyers-Ulam Stability for a Coupled System of Fractional Differential Equation With p-Laplacian...
    • 43. Zada, A., Alam, M., Riaz, U.: Analysis of q-fractional implicit boundary value problems having stieltjes integral conditions. Math. Meth....
    • 44. Zhang, F., Chen, G., Li, C., Kurths, J.: Chaos synchronization in fractional differential systems. Phil. Trans. R. Soc. A 371, 20120155,...
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