Hadamard Fractional Differential Equations on an Unbounded Domain with Integro-initial 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. 23, Nº 4, 2024
• Idioma: inglés
• DOI: 10.1007/s12346-024-01044-6
• Enlaces
  • Texto completo
• Resumen

  • In this paper, we introduce and investigate a Hadamard-type fractional differential equation on the interval (1,∞) equipped with a new class of logarithmic type integroinitial conditions. We apply the Leggett–Williams fixed point theorem and the concept of iterative positive solutions to establish the existence of solutions for the problem at hand. Our results are new and enrich the literature on Hadamard-type fractional differential equations on the infinite domain. Examples illustrating the main results are presented.

• Referencias bibliográficas
  • 1. Xu, C., Liu, Z., Li, P., Yan, J., Yao, L.: Bifurcation mechanism for fractional-order three-triangle multi-delayed neural networks. Neural...
  • 2. Xu, C., Liu, Z., Liao, M., Li, P., Xiao, Q., Yuan, S.: Fractional-order bidirectional associate memory (BAM) neural networks with multiple...
  • 3. Li, P., Gao, R., Xu, C., Li, Y., Akgül, A., Baleanu, D.: Dynamics exploration for a fractional-order delayed zooplankton-phytoplankton...
  • 4. Zhu, H., Peng, Y., Li, Y., Zeng, C.: Forward dynamics and memory effect in a fractional order chemostat minimal model with non-monotonic...
  • 5. Fallahgoul, H.A., Focardi, S.M., Fabozzi, F.J.: Fractional Calculus and Fractional Processes with Applications to Financial Economics....
  • 6. Kilbas, A.A., Srivastava, H.M., Trujillo, J.J.: Theory and Applications of Fractional Differential Equations, North-Holland Mathematics...
  • 7. Hadamard, J.: Essai sur letude des fonctions donnees par leur developpment de Taylor. J. Mat. Pure Appl. Ser. 8, 101–186 (1892)
  • 8. Ahmad, B., Alsaedi, A., Ntouyas, S.K., Tariboon, J.: Hadamard-Type Fractional Differential Equations. Inclusions and Inequalities. Springer,...
  • 9. Ardjouni, A.: Positive solutions for nonlinear Hadamard fractional differential equations with integral boundary conditions. AIMS Math....
  • 10. Subramanian, M., Alzabut, J., Baleanu, D., Samei, M.E., Zada, A.: Existence, uniqueness and stability analysis of a coupled fractional-order...
  • 11. Adjabi, Y., Samei, M.E., Matar, M.M., Alzabut, J.: Langevin differential equation in frame of ordinary and Hadamard fractional derivatives...
  • 12. Fahd, F., Abdeljawad, T., Baleanu, D.: Caputo-type modification of the Hadamard fractional derivatives. Adv. Differ. Equ. 2012, 142 (2012)
  • 13. Gambo, Y.Y., Jarad, F., Baleanu, D., Abdeljawad, T.: On Caputo modification of the Hadamard fractional derivatives. Adv. Differ. Equ....
  • 14. Liang, S., Zhang, J.: Existence of three positive solutions of m-point boundary value problems for some nonlinear fractional differential...
  • 15. Wang, G.: Explicit iteration and unbounded solutions for fractional integral boundary value problem on an infinite interval. Appl. Math....
  • 16. Zhai, C., Ren, J.: A coupled system of fractional differential equations on the half-line. Bound. Value Probl. Paper No. 117, 22 (2019)
  • 17. Liu, Y.: Existence and uniqueness of solutions for a class of initial value problems of fractional differential systems on half lines....
  • 18. Wang, G., Pei, K., Agarwal, R.P., Zhang, L., Ahmad, B.: Nonlocal Hadamard fractional boundary value problem with Hadamard integral and...
  • 19. Thiramanus, P., Ntouyas, S.K., Tariboon, J.: Positive solutions for Hadamard fractional differential equations on infinite domain. Adv....
  • 20. Pei, K., Wang, G., Sun, Y.: Successive iterations and positive extremal solutions for a Hadamard type fractional integro-differential...
  • 21. Zhang, W., Ni, J.: New multiple positive solutions for Hadamard-type fractional differential equations with nonlocal conditions on an...
  • 22. Cerdik, T.S., Deren, F.Y.: New results for higher-order Hadamard-type fractional differential equations on the half-line. Math. Meth....
  • 23. Hammad, H.A., Zayed, M.: Solving systems of coupled nonlinear Atangana–Baleanu-type fractional differential equations. Bound. Value Probl....
  • 24. Garra, R., Mainardi, F., Spada, G.: A generalization of the Lomnitz logarithmic creep law via Hadamard fractional calculus. Chaos Solitons...
  • 25. Saxena, R.K., Garra, R., Orsingher, E.: Analytical solution of space-time fractional telegraph-type equations involving Hilfer and Hadamard...
  • 26. Garra, R., Orsingher, E., Polito, F.: A note on Hadamard fractional differential equations with varying coefficients and their applications...
  • 27. Garra, R., Giusti, A., Mainardi, F., Pagnini, G.: Fractional relaxation with time-varying coefficient. Fract. Calc. Appl. Anal. 17, 424–439...
  • 28. Tarasov, V.E.: Entropy interpretation of Hadamard-type fractional operators: fractional cumulative entropy. Entropy 24, 1852 (2022). https://doi.org/10.3390/e24121852
  • 29. Wang, T., Wang, G., Yang, X.-J.: On a Hadamard-type fractional turbulent flow model with deviating arguments in a porous medium. Nonlinear...
  • 30. Wang, G., Ren, X., Zhang, L., Ahmad, B.: Explicit iteration and unique positive solution for a Caputo– Hadamard fractional turbulent flow...
  • 31. Liao, N.: On the logarithmic type boundary modulus of continuity for the Stefan problem: to the memory of Emmanuele DiBenedetto. Adv....
  • 32. Park, S.-H.: Blow-up for logarithmic viscoelastic equations with delay and acoustic boundary conditions. Adv. Nonlinear Anal. 12, 20220310,...
  • 33. Leggett, R.W., Williams, L.R.: Multiple positive fixed points of nonlinear operators on ordered Banach spaces. Indiana Univ. Math. J....
  • 34. Bai, Z., Ge, B.: Existence of three positive solutions for some second-order boundary value problems. Comput. Math. Appl. 48, 699–707...
  • 35. Rodríguez-López, J.: A fixed point index approach to Krasnosel’ski˘ı-Precup fixed point theorem in cones and applications. Nonlinear Anal....