Akcije

Mathematica Moravica
kako citirati ovaj članak
podeli ovaj članak
Direktan link

Metrika

  • citati u SCIndeksu: 0
  • citati u CrossRef-u:[8]
  • citati u Google Scholaru:[]
  • posete u poslednjih 30 dana:4
  • preuzimanja u poslednjih 30 dana:3

Sadržaj

članak: 1 od 1  
Mathematica Moravica
2020, vol. 24, br. 1, str. 109-122
Existence and Ulam stability results for nonlinear hybrid implicit Caputo fractional differential equations
(naslov ne postoji na srpskom)
Lachouri Adela, Ardjouni Abdelouahebb, Djoudi Ahcenea
aUniversity of Annaba, Department of Mathematics, Applied Mathematics Lab, Annaba, Algeria
bUniversity of Souk Ahras, Department of Mathematics and Informatics, Souk Ahras, Algeria

e-adresa: lachouri.adel@yahoo.fr, abd_ardjouni@yahoo.fr, adjoudi@yahoo.com
Ključne reči: Implicit fractional differential equations; Caputo fractional derivatives; fixed point theorems; existence; uniqueness; Ulam stability
Sažetak
(ne postoji na srpskom)
In this paper, we study the existence, uniqueness and estimate of solutions for nonlinear hybrid implicit Caputo fractional differential equations by using the contraction mapping principle and the generalization of Gronwall's inequality. After that, we also establish the Ulam stability for the problem at hand. Finally, an example is given to illustrate this work.
Reference

Abbas, S. (2011) Existence of solutions to fractional order ordinary and delay differential equations and applications. Electronic Journal of Differential Equations, (9): 1-11

Agarwal, R.P., Zhou, Y., He, Y. (2010) Existence of fractional neutral functional differential equations. Computers & Mathematics with Applications, 59(3): 1095-1100

1

Ahmad, B., Ntouyas, S.K. (2014) Initial value problems for hybrid Hadamard fractional equations. Electron. J. Differential Equations, 161: 1-8

Ahmad, B., Ntouyas, S.K. (2017) Existence and uniqueness of solutions for Caputo-Hadamard sequential fractional order neutral functional differential equations. Electronic Journal of Differential Equations, (36): 1-11

1

Aissani, K., Benchohra, M. (2019) Impulsive fractional differential inclusions with state-dependent delay. Mathematica Moravica, vol. 23, br. 2, str. 97-113

Ardjouni, A., Djoudi, A. (2021) Positive solutions for first-order nonlinear Caputo-Hadamard fractional relaxation differential equations. Kragujevac Journal of Mathematics, 45(6): 897-908

Ardjouni, A., Djoudi, A. (2019) Existence of positive periodic solutions for third-order nonlinear delay differential equations with variable coefficients. Mathematica Moravica, vol. 23, br. 2, str. 17-28

Ardjouni, A., Djoudi, A. (2019) Approximating Solutions of Nonlinear Hybrid Caputo Fractional Integro-Differential Equations via Dhage Iteration Principle. Ural Mathematical Journal, 5(1): 3-12

Ardjouni, A., Djoudi, A. (2019) Initial-value problems for nonlinear hybrid implicit Caputo fractional differential equations. Malaya Journal of Matematik, 7(2): 314-317

2

Ardjouni, A., Djoudi, A. (2015) Stability for nonlinear neutral integro-differential equations with variable delay. Mathematica Moravica, vol. 19, br. 2, str. 1-18

3

Ardjouni, A., Djoudi, A. (2014) Stability in nonlinear neutral differential equations with infinite delay. Mathematica Moravica, vol. 18, br. 2, str. 91-103

Ardjouni, A. (2019) Positive solutions for nonlinear Hadamard fractional differential equations with integral boundary conditions. AIMS Mathematics, 4(4): 1101-1113

Asawasamrit, S., Nithiarayaphaks, W., Ntouyas, S.K., Tariboon, J. (2019) Existence and Stability Analysis for Fractional Differential Equations with Mixed Nonlocal Conditions. Mathematics, 7(117): 1-11

1

Benchohra, M., Lazreg, J.E. (2015) On stability for nonlinear implicit fractional differential equations. Le Matematiche, 70(2): 49-61

Bohner, M., El-Morshedy, H.A., Grace, S.R., Sağer, I. (2019) Oscillation of second-order nonlinear difference equations with sublinear neutral term. Mathematica Moravica, vol. 23, br. 1, str. 1-10

Boulares, H., Ardjouni, A., Laskri, Y. (2017) Positive solutions for nonlinear fractional differential equations. Positivity, 21(3): 1201-1212

Boulares, H., Ardjouni, A., Laskri, Y. (2016) Stability in delay nonlinear fractional differential equations. Rend. Circ. Mat. Palermo, 65(2): 243-253

Chidouh, A., Guezane-Lakoud, A., Bebbouchi, R. (2016) Positive Solutions of the Fractional Relaxation Equation Using Lower and Upper Solutions. Vietnam Journal of Mathematics, 44(4): 739-748

Dan, H. (1981) Geometric theory of semilinear parabolic equations. Berlin-Heidelberg-New York: Springer-Verlag

Dhage, B.C. (2013) Hybrid fixed point theory in partially ordered normed linear spaces and applications to fractional integral equations. Differential Equations & Applications, 5(2): 155-184

Dhage, B.C., Lakshmikantham, V. (2010) Basic results on hybrid differential equations. Nonlinear Analysis: Hybrid Systems, 4(3): 414-424

Dhage, B.C., Dhage, S.B., Ntouyas, S.K. (2014) Approximating solutions of nonlinear hybrid differential equations. Applied Mathematics Letters, 34: 76-80

Diethelm, K. (2010) The Analysis of Fractional Differential Equations. u: Lecture Notes in Mathematics, Berlin-Heidelberg: Springer-Verlag

Ge, F., Kou, C. (2015) Asymptotic stability of solutions of nonlinear fractional differential equations of order 1 < a < 2. Journal of Shanghai Normal University, 44(3): 284-290

1

Ge, F., Kou, C. (2015) Stability analysis by Krasnoselskii's fixed point theorem for nonlinear fractional differential equations. Applied Mathematics and Computation, 257: 308-316

Guezane-Lakoud, A., Ramdane, S. (2018) Existence of solutions for a system of mixed fractional differential equations. Journal of Taibah University for Science, 12(4): 421-426

Haoues, M., Ardjouni, A., Djoudi, A. (2018) Existence, interval of existence and uniqueness of solutions for nonlinear implicit Caputo fractional differential equations. Transylvanian Journal of Mathematics and Mechanics, 10(1): 9-13

1

Hocine, G., Abdelouaheb, A., Ahcene, D. (2018) Positive periodic solutions of second-order nonlinear neutral differential equations with variable coefficients. Mathematica Moravica, vol. 22, br. 2, str. 69-82

4

Kilbas, A.A., Srivastava, H.M., Trujillo, J.J. (2006) Theory and Applications of Fractional Differential Equations. Amsterdam: Elsevier Science

Kou, C., Zhou, H., Yan, Y. (2011) Existence of solutions of initial value problems for nonlinear fractional differential equations on the half-axis. Nonlinear Analysis: Theory, Methods & Applications, 74(17): 5975-5986

Kucche, K.D., Sutar, S.T. (2018) On existence and stability results for nonlinear fractional delay differential equations. Boletim da Sociedade Paranaense de Matemática, 36(4): 55-75

Lakoud, A., Khaldi, R., Kılıçman, A. (2017) Existence of solutions for a mixed fractional boundary value problem. Advances in Difference Equations, 2017(164): 1-9

4

Lakshmikantham, V., Vatsala, A.S. (2008) Basic theory of fractional differential equations. Nonlinear Analysis: Theory, Methods & Applications, 69(8): 2677-2682

Li, N., Wang, C. (2013) New existence results of positive solution for a class of nonlinear fractional differential equations. Acta Mathematica Scientia, 33(3): 847-854

23

Podlubny, I. (1999) Fractional Differential Equations. San Diego, CA: Academic Press

1

Rus, I.A. (2010) Ulam Stabilities of ordinary differential equations in a Banach space. Carpathian J. Math., 26(1): 103-107

Smart, D.R. (1974) Fixed Point Theorems. u: Cambridge Tracts in Mathematics, London-New York: Cambridge University Press, 66

Wang, J., Lv, L., Zhou, Y. (2012) New concepts and results in stability of fractional differential equations. Communications in Nonlinear Science and Numerical Simulation, 17(6): 2530-2538

2

Wang, J., Lv, L., Zhou, Y. (2011) Ulam stability and data dependence for fractional differential equations with Caputo derivative. Electronic Journal of Qualitative Theory of Differential Equations, (63): 1-10

Zhang, S. (2000) The Existence of a Positive Solution for a Nonlinear Fractional Differential Equation. Journal of Mathematical Analysis and Applications, 252(2): 804-812