Article ID: MTJPAM-D-21-00020

Title: Analytic Solvability of a Class of Symmetric Nonlinear Second Order Differential Equations

Montes Taurus J. Pure Appl. Math. / ISSN: 2687-4814

Article ID: MTJPAM-D-21-00020; Volume 4 / Issue 3 / Year 2022 (Special Issue), Pages 80-92

Document Type: Research Paper

Author(s): Rabha Waell Ibrahim a

aIEEE: 94086547, Kuala Lumpur, 59200, Malaysia

Received: 18 February 2021, Accepted: 25 September 2021, Published: 27 October 2021.

Corresponding Author: Rabha Waell Ibrahim (Email address:

Full Text: PDF


In this study, we introduce a solvability of special type of symmetric algebraic differential equations (SADEs) in virtue of geometric function theory by considering a symmetric differential operator. The analytic solutions of the SADEs are considered by utilizing the Caratheodory functions joining the subordination concept. A class of Caratheodory functions involving special functions gives the upper bound solution.

Keywords: Analytic function, Subordination, Univalent function, Open unit disk, Differential equations

  1. E. J. Beggs and S. Majid, Quantum complex structures, Quantum Riemannian Geometry, Springer, Cham, 527–564, 2020.
  2. C. Fernando, P. Chartier, A. Escorihuela-Tomas and Y. Zhang, Compositions of pseudo-symmetric integrators with complex coefficients for the numerical integration of differential equations, Journal of Computational and Applied Mathematics 113006, 1–19, 2020.
  3. G. G. Gary, Research questions on meromorphic functions and complex differential equations, Computational Methods and Function Theory 17 (2), 195–209, 2017.
  4. R. W. Ibrahim, Fractional algebraic nonlinear differential equations in a complex domain, Afrika Matematika 26 (3-4), 385–397, 2015.
  5. R. W. Ibrahim and D. Baleanu, On a combination of fractional differential and integral operators associated with a class of normalized functions, AIMS Mathematics 6 (4), 4211–4226, 2021.
  6. R. W. Ibrahim and D. Baleanu, On quantum hybrid fractional conformable differential and integral operators in a complex domain, RACEF-Naturales. Serie A. Matematicas 115 (1), 1–13, 2021.
  7. R. W. Ibrahim and D. Baleanu, Entire solutions of a class of algebraic Briot-Bouquet differential equations utilizing majority concept, Advances in Difference Equations 1, 1–12, 2020.
  8. R. W. Ibrahim and M. Darus, New symmetric differential and integral operators defined in the complex domain, Symmetry 11 (7), 906, 2019.
  9. R. W. Ibrahim and M. Darus, On a new solution of fractional differential equation using complex transform in the unit disk, Mathematical and Computational Applications 19 (2), 152–160, 2014.
  10. R. W. Ibrahim, R. M. Elobaid and S. J. Obaiys, On the connection problem for Painleve differential equation in view of geometric function theory, Mathematics 8 (7), 1198, 2020.
  11. R. W. Ibrahim and J. M. Jahangiri, Boundary fractional differential equation in a complex domain, Boundary Value Problems 2014 (1), 1–11, 2014.
  12. Y. Masafumi, Monodromy of confluent hypergeometric system with two irregular singular points (Algebraic analytic methods in complex partial differential equations), Kyoto University Research Information Repository 2020, 129–136, 2017.
  13. S. S. Miller and P. T. Mocanu, Differential subordinations: theory and applications, CRC Press, 2000.
  14. S. Norbert, Nevanlinna theory, normal families, and algebraic differential equations, Cham: Springer, 2017.
  15. W. Qiongyan, M. Liu and N. Li, On algebraic differential equations concerning the Riemann-zeta function and the Euler-gamma function, arXiv preprint arXiv:2005, 2020.
  16. S. Ruscheweyh, Convolutions in geometric function theory, Vol. 83, Gaetan Morin Editeur Ltee, 1982.
  17. G. Yongyi, X. Zheng and F. Meng, Painleve analysis and abundant meromorphic solutions of a class of nonlinear algebraic differential equations, Mathematical Problems in Engineering 2019, 1–12, 2019.