Abstract
The recently proposed complex number differential operator is used in formulating ordinary differential equations for the first time. The differential operator definition is totally different than the real number differentiation of complex valued functions. The basic definitions and properties of the differential operator are given first. Various linear differential equations are treated containing the new differential operator. Associated theorems with the differential equations are given. Then the nonlinear differential equations of complex valued functions are treated. In separated form, the complex differential operator equations lead to nonlinear coupled real valued equations. Various nonlinear differential equations with complex number derivatives are written and solved. Finally, the geometric meaning of the new differential operator is discussed in the last section. A physical example involving complex derivatives are given. The topic may lead to a broad range of applications in several branches of sciences that employ differential equations for mathematical modelling of their problems.
Recommended Citation
Pakdemirli, Mehmet
(2023).
(R2061) Differential Equations Involving a New Definition of Complex Number Derivatives,
Applications and Applied Mathematics: An International Journal (AAM), Vol. 19,
Iss.
2, Article 11.
Available at:
https://digitalcommons.pvamu.edu/aam/vol19/iss2/11