PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
Powiadomienia systemowe
  • Sesja wygasła!
Tytuł artykułu

Integral solutions of nondense impulsive conformable-fractional differential equations with nonlocal condition

Identyfikatory
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In this paper, a class of nondense impulsive differential equations with nonlocal condition in the frame of the conformable fractional derivative is studied. The abstract results concerning the existence, uniqueness and stability of the integral solution are obtained by using the extrapolation semigroup approach combined with some fixed point theorems.
Wydawca
Rocznik
Strony
187--197
Opis fizyczny
Bibliogr. 39 poz.
Twórcy
  • Department of Mathematics, Sultan Moulay Slimane University, BP 523, 23000 Beni Mellal, Morocco
autor
  • Department of Mathematics, Sultan Moulay Slimane University, BP 523, 23000 Beni Mellal, Morocco
  • Department of Mathematics, Sultan Moulay Slimane University, BP 523, 23000 Beni Mellal, Morocco
Bibliografia
  • [1] T. Abdeljawad, On conformable fractional calculus, J. Comput. Appl. Math. 279 (2015), 57-66.
  • [2] M. Adimy, M. Alia and K. Ezzinbi, Functional differential equations with unbounded delay in extrapolation spaces, Electron. J. Differential Equations 2014 (2014), Paper No. 180.
  • [3] V. V. Au, Y. Zhou, N. H. Can and N. T. Tuan, Regularization of a terminal value nonlinear diffusion equation with conformable time derivative, J. Integral Equations Appl. 32 (2020), no. 4, 397-416.
  • [4] M. Benchohra, J. Henderson and S. Ntouyas, Impulsive Differential Equations and Inclusions, Contemp. Math. Appl. 2, Hindawi Publishing, New York, 2006.
  • [5] T. T. Binh, N. H. Luc, D. O’Regan and N. H. Can, On an initial inverse problem for a diffusion equation with a conformable derivative, Adv. Difference Equ. 2019 (2019), Paper No. 481.
  • [6] M. Bouaouid, M. Atraoui, K. Hilal and S. Melliani, Fractional differential equations with nonlocal-delay condition, J. Adv. Math. Stud. 11 (2018), no. 2, 214-225.
  • [7] M. Bouaouid, M. Hannabou and K. Hilal, Nonlocal conformable-fractional differential equations with a measure of noncompactness in Banach spaces, J. Math. 2020 (2020), Article ID 5615080.
  • [8] M. Bouaouid, K. Hilal and S. Melliani, Nonlocal conformable fractional Cauchy problem with sectorial operator, Indian J. Pure Appl. Math. 50 (2019), no. 4, 999-1010.
  • [9] M. Bouaouid, K. Hilal and S. Melliani, Nonlocal telegraph equation in frame of the conformable time-fractional derivative, Adv. Math. Phys. 2019 (2019), Article ID 7528937.
  • [10] M. Bouaouid, K. Hilal and S. Melliani, Sequential evolution conformable differential equations of second order with nonlocal condition, Adv. Difference Equ. 2019 (2019), Paper No. 21.
  • [11] M. Bouaouid, K. Hilal and S. Melliani, Existence of mild solutions for conformable fractional differential equations with nonlocal conditions, Rocky Mountain J. Math. 50 (2020), no. 3, 871-879.
  • [12] L. Byszewski, Theorems about the existence and uniqueness of solutions of a semilinear evolution nonlocal Cauchy problem, J. Math. Anal. Appl. 162 (1991), no. 2, 494-505.
  • [13] W. S. Chung, Fractional Newton mechanics with conformable fractional derivative, J. Comput. Appl. Math. 290 (2015), 150-158.
  • [14] G. Da Prato and E. Sinestrari, Differential operators with non dense domain, Ann. Sc. Norm. Super. Pisa Cl. Sci. (4) 14 (1987), 285-344.
  • [15] K. Deng, Exponential decay of solutions of semilinear parabolic equations with nonlocal initial conditions, J. Math. Anal. Appl. 179 (1993), no. 2, 630-637.
  • [16] A. El-Ajou, A modification to the conformable fractional calculus with some applications, Alexandria Eng. J. 59 (2020), no. 4, 2239-2249.
  • [17] H. Eltayeb, I. Bachar and M. Gad-Allah, Solution of singular one-dimensional Boussinesq equation by using double conformable Laplace decomposition method, Adv. Difference Equ. 2019 (2019), Paper No. 293.
  • [18] H. Eltayeb and S. Mesloub, A note on conformable double Laplace transform and singular conformable pseudoparabolic equations, J. Funct. Spaces 2020 (2020), Article ID 8106494.
  • [19] K. J. Engel and R. Nagel, One-Parameter Semigroups for Linear Evolution Equations, Grad. Texts in Math. 194, Springer, Berlin, 2001.
  • [20] K. Ezzinbi and J. H. Liu, Nondensely defined evolution equations with nonlocal conditions, Math. Comput. Modelling 36 (2002), no. 9-10, 1027-1038.
  • [21] R. Khalil, M. Al Horani, A. Yousef and M. Sababheh, A new definition of fractional derivative, J. Comput. Appl. Math. 264 (2014), 65-70.
  • [22] A. A. Kilbas, H. M. Srivastava and J. J. Trujillo, Theory and Applications of Fractional Differential Equations, North-Holland Math. Stud. 204, Elsevier Science, Amsterdam, 2006.
  • [23] V. Lakshmikantham, D. D. Ba˘ınov and P. S. Simeonov, Theory of Impulsive Differential Equations, Ser. Mod. Appl. Math. 6, World Scientific, Teaneck, 1989.
  • [24] J. Liang, J. H. Liu and T.-J. Xiao, Nonlocal impulsive problems for nonlinear differential equations in Banach spaces, Math. Comput. Modelling 49 (2009), no. 3-4, 798-804.
  • [25] L. Martínez, J. J. Rosales, C. A. Carreño and J. M. Lozano, Electrical circuits described by fractional conformable derivative, International Journal of Circuit Theory and Applications 46 (2018), no. 5, 1091-1100.
  • [26] K. S. Miller and B. Ross, An Introduction to the Fractional Calculus and Fractional Differential Equations, John Wiley & Sons, New York, 1993.
  • [27] G. M. Mophou, Existence and uniqueness of mild solutions to impulsive fractional differential equations, Nonlinear Anal. 72 (2010), no. 3-4, 1604-1615.
  • [28] G. M. Mophou and G. M. N’Guérékata, On integral solutions of some nonlocal fractional differential equations with nondense domain, Nonlinear Anal. 71 (2009), no. 10, 4668-4675.
  • [29] K. B. Oldham and J. Spanier, The Fractional Calculus, Academic Press, New York, 1974.
  • [30] W. E. Olmstead and C. A. Roberts, The one-dimensional heat equation with a nonlocal initial condition, Appl. Math. Lett. 10 (1997), no. 3, 89-94.
  • [31] A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, Appl. Math. Sci. 44, Springer, New York, 1983.
  • [32] I. Podlubny, Fractional Differential Equations, Math. Sci. Eng. 198, Academic Press, San Diego, 1999.
  • [33] S. G. Samko, A. A. Kilbas and O. I. Marichev, Fractional Integrals and Derivatives. Theory and Applications, Gordon & Breach Science, Yverdon, 1993.
  • [34] H. R. Thieme, “Integrated semigroups” and integrated solutions to abstract Cauchy problems, J. Math. Anal. Appl. 152 (1990), no. 2, 416-447.
  • [35] N. H. Tuan, T. N. Thach, N. H. Can and D. O’Regan, Regularization of a multidimensional diffusion equation with conformable time derivative and discrete data, Math. Methods Appl. Sci. (2019), DOI 10.1002/mma.6133.
  • [36] X. Wang, J. Wang and M. Fečkan, Controllability of conformable differential systems, Nonlinear Anal. Model. Control 25 (2020), no. 4, 658-674.
  • [37] S. Yang, L. Wang and S. Zhang, Conformable derivative: Application to non-Darcian flow in low-permeability porous media, Appl. Math. Lett. 79 (2018), 105-110.
  • [38] S. T. Zavalishchin, Impulse dynamic systems and applications to mathematical economics, Dynam. Systems Appl. 3 (1994), no. 3, 443-449.
  • [39] D. Zhao and M. Luo, General conformable fractional derivative and its physical interpretation, Calcolo 54 (2017), no. 3, 903-917.
Uwagi
Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2021)
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-04fee76c-d2d8-4008-b99a-51592d8523f3
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.