New problem of Lane Emden type via fractional calculus
*Ameth NdiayeCorresponding authorameth1.ndiaye@ucad.edu.snDépartement de MathematiquesFaculté des Sciences et Technologies de l’Education et la FormationDakar, SénégalUniversité Cheikh Anta DiopView full profile → , Yazid GouariLaboratory of Pure and Applied MathematicsFaculty of Exacte Scienes and Informatics27000 MostaganemUniversity of MostaganemAlgeriaView full profile → , Zoubir Dahmanizzdahmani@yahoo.frLaboratory of Pure and Applied MathematicsFaculty of Exacte Scienes and Informatics27000 MostaganemUniversity of MostaganemAlgeria0000-0003-4659-0723View full profile →
* Corresponding author · click or hover a name for details
- Received:
- 05 Aug 2020
- Accepted:
- 05 Dec 2020
- Published Online:
- 01 Mar 2023
- Article type:
- A
- Language:
- EN
- Article no.:
- JIM-1231
- Pages:
- 145–161
Abstract
Keywords
Subject Classifications
References
[1] R. P. Agarwal, D. O’Regan and S. Stanĕk: Positive Solutions for Mixed Problems of Singular Fractional Differential Equations, Mathematische Nachrichten., Vol. 285, No. 1, (2012).
[2] Z. Bai , W. Sun: Existence and Multiplicity of Positive Solutions for Singular Fractional Boundary Value Problems, Computers & Mathematics with Applications., Vol. 63, No. 9, (2012).
[3] D. Baleanu, H. Mohammadi, S. Rezapour: The existence of solutions for a nonlinear mixed problem of singular fractional differential equations, Adv. Differ. Equ. 2013, Article ID 359 (2013).
[4] Z. Bekkouche, Z. Dahmani and G. Zhang: Solutions and Stabilities for a 2D-Non Homogeneous Lane-Emden Fractional System, Int. J. Open Problems Compt. Math., Vol. 11, No. 2, (2018).
[5] M. Cakmak:Refinements of bullen-type inequalities for s-convex functions via Riemann-Liouville fractional integrals involving Gauss hypergeometric function, J. Interdiscip. Math., Vol. 22 No. 6, 975-989 (2019).
[6] Y. Gouari, Z. Dahmani, A. Ndiaye : A generalized sequential problem of Lane Emden type via fractional calculus, Moroccan J. Pure Appl. Anal. Vol. 6; No. 2, 168-183 (2020)
[7] M. Houas, Z. Dahmani, M. Z. Sarikaya. Some integral inequalities for ( k, s ) -Riemann-Liouville fractional operators, J. Interdiscip. Math., Vol. 21, No7-8, 1575-1585 (2018).
[8] R.W. Ibrahim: Existence of Nonlinear Lane-Emden Equation of Fractional Order, Miskolc Mathematical Notes, Vol. 13, No. 1, (2012).
[9] R.W. Ibrahim: Stability of A Fractional Differential Equation, International Journal of Mathematical, Computational, Physical and Quantum Engineering., Vol. 7, No. 3, (2013).
[10] A.A. Kilbas, H.M. Srivastava and J.J. Trujillo: Theory and Applications of Fractional Differential Equations, Elsevier B.V., Amsterdam, The Netherlands, (2006).
[11] Z. Lin, J. R. Wang New Riemann-Liouville fractional Hermite-Hadamard inequalities via two kinds of convex functions, J. Interdiscip. Math., Vol. 20, No. 2, 357-382 (2017).
[12] S.M. Mechee and N. Senu: Numerical Study of Fractional Differential Equations of Lane-Emden Type by Method of Collocation, Applied Mathematics., 3, (2012).
[13] K.S. Miller and B. Ross: An Introduction to the Fractional Calculus and Fractional Differential Equations, Wiley, New York., (1993).
[14] A. Mohammadi, N. Aghazadeh, S. Rezapour : Haar wavelet collocation method for solving singular and nonlinear fractional time-dependent Emden-Fowler equations with initial and boundary conditions, Math. Sci., (2019).
[15] A. Ndiaye, A Nonlinear Implicit Fractional Equation with Caputo Derivative, J. Math., 2021, Article ID 5547003, 9 pp.
[16] S.A. Okunuga, J.O. Ehigie and A.B. Sofoluwe: Treatment of Lane-Emden Type Equations via Second Derivative Backward Differentiation Formula Using Boundary Value Technique, Proceedings of the World Congress on Engineering., Vol. IWCE, (2012).
[17] J. Serrin , H. Zou: Existence of Positive Solutions of Lane-Emden Systems Atti Del Sem, Mat. Fis. Univ. Modena., 46 (Suppl), (1998).
[18] L. Tabharit, Z. Dahmani Solvability of a boundary value problem with caputo derivative, J. Interdiscip. Mathematics, Vol. 19, No. 5-6, 907-915 (2017).




