Complex conformable derivative
- 84 Downloads
In this study, we introduce a new complex conformable derivative and integral with noninteger order α which coincides the classical complex derivative and integral for α = 1. We examine basic properties of these newly defined derivative and integral such as Cauchy-Riemann equations, conformability and fundamental theorem of complex conformable integral. As an application of the new operators, we solve some types of complex conformable differential equations.
KeywordsComplex conformable derivative Complex conformable integral Conformability
The authors would like to thank Prof. Ali Güven for his valuable contributions on this study.
This research is supported by Balikesir University Research Grant No. Bap 2018/023.
- Ahlfors Complex Analysis: An introduction of the theory of analytic functions of one complex variable McGraw–Hill, New York (1966)Google Scholar
- Brown JW, Churchill RV (2004) Complex variables and applications. McGraw-Hill, New YorkGoogle Scholar
- Caputo M, Fabrizio M (2015) A new definition of fractional derivative without singular kernel. Progr Fract Differ Appl 1:73–85Google Scholar
- Evirgen F (2011) Multistage adomian decomposition method for solving NLP problems over a nonlinear fractional dynamical system. J Comput Nonlinear Dyn 156:6Google Scholar
- Gamelin TW (2003) Complex Analysis. Springer, BerlinGoogle Scholar
- Kilbas AA, Srivastava HM, Trujillo JJ (2006) Theory and applications of fractional differential equations. Elsevier B. V, AmsterdamGoogle Scholar
- Mandic DP (2000) The use of Möbius transformations in neural networks and signal processing. In Neural Networks for Signal Processing-Proocedings of the IEEE Workshop 1:185–194 Google Scholar
- Ponnusamy S, Silverman H (2006) Complex variables with applications. Birkhauser, BostonGoogle Scholar
- Rudin W (1987) Real and complex analysis, 3rd edn. McGraw–Hill, New YorkGoogle Scholar
- Schinzinger R, Laura PAA (1991) Conformal mapping methods and applications. Elsevier Science Pub, AmsterdamGoogle Scholar
- Yavuz M (2018) Novel solution methods for initial boundary value problems of fractional order with conformable differentiation. Int J Optim Control Theor Appl IJOCTA 8:1–7Google Scholar
- Zill A, Shanahan P (2009) First course in complex analysis with applications. Jones\& Bartlett Learning, BurlingtonGoogle Scholar