On a Mixed Nonlinear Fractional Boundary Value Problem with a New Class of Closed Integral Boundary Conditions

• Bashir Ahmad ^[1] ; Manal Alnahdi ^[1] ; Sotiris K. Ntouyas ^[2] ; Ahmed Alsaedi ^[1]
  1. [1] King Abdulaziz University

     King Abdulaziz University

     Arabia Saudí

     
  2. [2] University of Ioannina

     University of Ioannina

     Dimos Ioánnina, Grecia

     
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 22, Nº 3, 2023
• Idioma: inglés
• DOI: 10.1007/s12346-023-00781-4
• Enlaces
  • Texto completo
• Resumen

  • In this paper, we investigate the existence of solutions for a fractional integrodifferential equation with mixed nonlinearities subject to a new class of nonlocal closed integral boundary conditions. The proposed problem contains a right Liouville– Caputo fractional derivative operator and mixed Riemann-Liouville integral operators.

    The standard fixed point theorems are applied to derive the desired results, which are well-illustrated with examples. Some interesting observations are presented.

• Referencias bibliográficas
  • 1. Feng, M., Zhang, X., Ge, W.: Existence theorems for a second order nonlinear differential equation with nonlocal boundary conditions and...
  • 2. Zheng, L., Zhang, X.: Modeling and Analysis of Modern Fluid Problems. Mathematics in Science and Engineering, Elsevier/Academic Press,...
  • 3. Nicoud, F., Schfonfeld, T.: Integral boundary conditions for unsteady biomedical CFD applications. Int. J. Numer. Meth. Fluids 40, 457–465...
  • 4. Ciegis, R., Bugajev, A.: Numerical approximation of one model of the bacterial self-organization. ˇ Nonlinear Anal. Model Control 17, 253–270...
  • 5. Yusufoglu, E., Turhan, I.: A mixed boundary value problem in orthotropic strip containing a crack. J. Franklin Inst. 349, 2750–2769 (2012)
  • 6. Renterghem, T.V., Botteldooren, D., Verheyen, K.: Road traffic noise shielding by vegetation belts of limited depth. J. Sound Vib. 331,...
  • 7. Whyburn, W.M.: Differential equations with general boundary conditions. Bull. Am. Math. Soc. 48, 692–704 (1942)
  • 8. Conti, R.: Recent trends in the theory of boundary value problems for ordinary differential equations. Boll. Un. Mat. Ital. 22, 135–178...
  • 9. Ahmad, B., Ntouyas, S.K.: Nonlocal Nonlinear Fractional-Order Boundary Value Problems. World Scientific, Singapore (2021)
  • 10. Henderson, J., Luca, R., Tudorache, A.: On a system of fractional differential equations with coupled integral boundary conditions, Fract....
  • 11. Agarwal, R., Hristova, S., O’Regan, D.: Integral presentations of the solution of a boundary value problem for impulsive fractional integro-differential...
  • 12. Peng, L., Zhou, Y.: The existence of mild and classical solutions for time fractional Fokker-Planck equations. Monatsh. Math. 199, 377–410...
  • 13. Kirane, M., Abdeljabbar, A.: Nonexistence of global solutions of systems of time fractional differential equations posed on the Heisenberg...
  • 14. Webb, J.R.L., Infante, G.: Positive solutions of nonlocal boundary value problems involving integral conditions. NoDEA Nonlinear Diff....
  • 15. Ahmad, B., Alruwaily, Y., Ntouyas, S.K., Alsaedi, A.: Existence and stability results for a fractional order differential equation with...
  • 16. Lin, L., Liu, Y., Zhao, D.: Study on implicit-type fractional coupled system with integral boundary conditions. Mathematics 9(4), 300...
  • 17. Shivanian, E.: Error estimate and stability analysis on the study of a high-order nonlinear fractional differential equation with Caputo-derivative...
  • 18. Agarwal, R.P., Assolami, A., Alsaedi, A., Ahmad, B.: Existence results and Ulam-Hyers stability for a fully coupled system of nonlinear...
  • 19. Wongcharoen, A., Ntouyas, S.K., Wongsantisuk, P., Tariboon, J.: Existence results for a nonlocal coupled system of sequential fractional...
  • 20. Kucche, K.D., Mali, A.D.: On the nonlinear (k,ψ)-Hilfer fractional differential equations. Chaos Solitons Fractals 152, 111335 (2021)
  • 21. Bouacida, I., Kerboua, M., Segni, S.: Controllability results for Sobolev type ψ-Hilfer fractional backward perturbed integro-differential...
  • 22. Panneer, S.A., Govindaraj, V.: Reachability of fractional dynamical systems with multiple delays in control using ψ-Hilfer pseudo-fractional...
  • 23. Yang, Q., Bai, C., Yang, D.: Finite-time stability of nonlinear stochastic ψ-Hilfer fractional systems with time delay. AIMS Math. 7,...
  • 24. Salim, A., Benchohra, M., Graef, J.R., Lazreg, J.E.: Initial value problem for hybrid ψ-Hilfer fractional implicit differential equations....
  • 25. Ntouyas, S.K., Ahmad, B., Nuchpong, C., Tariboon, J.: On (k,ψ)-Hilfer fractional differential equations and inclusions with mixed (k,ψ)-derivative...
  • 26. Ntouyas, S.K., Ahmad, B., Tariboon, J., Alhodaly, M.S.: Nonlocal integro-multi-point (k,ψ)-Hilfer type fractional boundary value problems....
  • 27. Ahmad, B., Alnahdi, M., Ntouyas, S.K.: Existence results for a differential equation involving the right Caputo fractional derivative...
  • 28. Ivashkevich, E.V.: Boundary height correlations in a two-dimensional Abelian sandpile. J. Phys. A Math. Gen. 27, 3643 (1994)
  • 29. Piroux, G., Ruelle, P.: Boundary height fields in the Abelian sandpile model. J. Phys. A Math. Gen. 38, 1451 (2005)
  • 30. Azimi-Tafreshi, N., Dashti-Naserabadi, H., Moghimi-Araghi, S., Ruelle, P.: The Abelian sandpile model on the honeycomb lattice. J. Stat....
  • 31. Donatelli, M., Serra-Capizzano, S.: Antireflective boundary conditions for deblurring problems, J. Electr. Comput. Eng. 2010 , Article...
  • 32. Li, X., Robertsson, J., Curtis, A., van Manen1, D.: Internal absorbing boundary conditions for closedaperture wavefield decomposition...
  • 33. Mohammadimehr, M., Okhravi, S.V., Alavi, S.M.A.: Free vibration analysis of magneto-electro-elastic cylindrical composite panel reinforced...
  • 34. Ahmad, B., Nieto, J.J., Pimentel, J.: Some boundary value problems of fractional differential equations and inclusions. Comput. Math....
  • 35. Setukha, A.V.: On the three-dimensional Neumann boundary value problem with a generalized boundary condition in a domain with a smooth...
  • 36. Wang, G., Ahmad, B., Zhang, L.: Existence results for nonlinear fractional differential equations with closed boundary conditions and...
  • 37. Ergoren, H., Kilicman, A.: Some existence results for impulsive nonlinear fractional differential equations with closed boundary conditions....
  • 38. Kilbas, A.A., Srivastava, H.M., Trujillo, J.J.: Theory and Applications of Fractional Differential Equations, North-Holland Mathematics...
  • 39. Krasnosel’ski˘ı, M.A.: Two remarks on the method of successive approximations. Uspekhi Mat. Nauk. 10, 123–127 (1955)
  • 40. Granas, A., Dugundji, J.: Fixed Point Theory, Springer, New York, NY, USA (2005)