A class of nonlinear singular differential equations

References

• 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), pp. 27–41. doi: 10.1002/mana.201000043
   Web of Science ®Google Scholar
• Z. Bai and W. Sun: Existence and Multiplicity of Positive Solutions for Singular Fractional Boundary Value Problems, Computers & Mathematics with Applications., Vol. 63, No. 9, (2012), pp. 1369–1381. doi: 10.1016/j.camwa.2011.12.078
   Web of Science ®Google Scholar
• 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).
   Google Scholar
• Z. Dahmani and M.Z. Sarikaya: On A Generalized Lane-Emden Fractional Differential System and its D–Stability, Journal of Advanc. Resear. Dynam. Contr. Syst., To Appear in 2016.
   Google Scholar
• Z. Dahmani and A. Taieb: New Existence and Uniqueness Results For High Dimensional Fractional Differential Systems, Facta Nis Ser. Math. Inform., Vol. 30, No. 3, (2015), pp. 281-293.
   Web of Science ®Google Scholar
• Z. Dahmani and A. Taieb: Solvability For High Dimensional Fractional Differential Systems With High Arbitrary Orders, Journal of Advanced Scientific Research in Dynamical and Control Systems., Vol. 7, No. 4, (2015), pp. 51-64.
   Google Scholar
• Z. Dahmani and A. Taieb: A Coupled System of Fractional Differential Equations Involing Two Fractional Orders, ROMAI Journal., Vol. 11, No. 2, (2015), pp. 141-177.
   Google Scholar
• Z. Dahmani and A. Taieb: Solvability of A Coupled System of Fractional Differential Equations with Periodic and Antiperiodic Boundary Conditions, PALM Letters., No. 5, (2015), pp. 29-36.
   Google Scholar
• Z. Dahmani, A. Taieb and N. Bedjaoui: Solvability and Stability for Nonlinear Fractional Integro-Differential Systems of High Fractional Orders, Facta Nis Ser. Math. Inform., Vol. 31, No. 3, (2016), pp. 629–644
   Web of Science ®Google Scholar
• R. Emden: Gaskugeln, Teubner, Leipzig and Berlin. 1907.
   Google Scholar
• R.W. Ibrahim: Stability of A Fractional Differential Equation, International Journal of Mathematical, Computational, Physical and Quantum Engineering., Vol. 7, No. 3, (2013), pp. 300-305.
   Google Scholar
• R.W. Ibrahim: Existence of Nonlinear Lane-Emden Equation of Fractional Order, Miskolc Mathematical Notes, Vol. 13, No. 1, (2012), pp. 39–52. doi: 10.18514/MMN.2012.453
   Web of Science ®Google Scholar
• A.A. Kilbas, H.M. Srivastava and J.J. Trujillo: Theory and Applications of Fractional Differential Equations, Elsevier B.V., Amsterdam, The Netherlands, (2006).
   Google Scholar
• C. Li and S. Sarwar: Existence and Continuation of Solutions for Caputo Type Fractional Differential Equations, Electron. J. Differential Equations., Vol. 2016, No. 207, (2016), 14 pp.
   Google Scholar
• S.M. Mechee and N. Senu: Numerical Study of Fractional Differential Equations of Lane-Emden Type by Method of Collocation, Applied Mathematics., 3, (2012), pp. 851-856. doi: 10.4236/am.2012.38126
   Google Scholar
• K.S. Miller and B. Ross: An Introduction to the Fractional Calculus and Fractional Differential Equations, Wiley, New York., (1993).
   Google Scholar
• 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), July 4–6, 2012, London, U.K.
   Google Scholar
• J. Serrin and H. Zou: Existence of Positive Solutions of Lane-Emden Systems Atti Del Sem, Mat. Fis. Univ. Modena., 46 (Suppl), (1998), pp. 369-380.
   Google Scholar
• A. Taieb and Z. Dahmani: A Coupled System of Nonlinear Differential Equations Involing m Nonlinear Terms, Georjian Math. Journal., Vol. 23, No. 3, (2016), pp. 447–458.
   Google Scholar
• A. Taieb and Z. Dahmani: A New Problem of Singular Fractional Differential Equations, Journal of Dynamical Systems and Geometric Theory., Vol. 14, No. 2, (2016), pp. 161-183.
   Web of Science ®Google Scholar
• A. Taieb and Z. Dahmani: On Singular Fractional Differential Systems and Ulam-hyers Stabilities, International Journal of Modern Mathematical Sciences., Vol.14, No. 3, (2016), pp. 262-282.
   Google Scholar
• A. Taieb and Z. Dahmani: The High Order Lane-Emden Fractional Differential System: Existence, Uniqueness and Ulam Stabilities, Kragujevac Journal of Mathematics., Vol. 40, No. 2, (2016), pp. 238–259. doi: 10.5937/KgJMath1602238A
   Web of Science ®Google Scholar
• A. Taieb and Z. Dahmani: Fractional System of Nonlinear Integro-Differential Equations, FCAJ Journal., To Appear in 2019.
   Google Scholar
• A. Taieb: Several Results for High Dimensional Singular Fractional Systems Involving n2-Caputo Derivatives, Malaya Journal of Matematik., To Appear in 2018.
   Google Scholar
• L. Tabharit, Z. Dahmani: Solvability of a boundary value problem with caputo derivative, Journal of Interdisciplinary Mathematics, 19:5-6, (2016), pp 907-915, DOI: 10.1080/09720502.2014.881136
   Web of Science ®Google Scholar