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Open Access A

New problem of Lane Emden type via fractional calculus

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pp. 145–161Vol. 26Issue 2March 2023DOI: 10.47974/JIM-1231XML
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

We study a nonlinear singular differential equation of Lane Emden type. The problem used the Caputo derivatives and Riemann-Liouville integrals. We first prove an existence and uniqueness result. Another main result is established. At the end, the discussion of two examples to show the applicability of the main results is given. This paper has some elationship with some other papers that have already been published by the same authors.

Keywords

Subject Classifications

(2010) 30C4539B7239B82

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).

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