Browsing by Author "Ilie, M."

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Citation Count: Hosseini, K...et al. (2020). "A detailed study on a new (2+1)-dimensional mKdV equation involving the Caputo-Fabrizio time-fractional derivative", Advances in Difference Equations, Vol. 2020, No. 1.
A detailed study on a new (2+1)-dimensional mKdV equation involving the Caputo-Fabrizio time-fractional derivative
(2020) Hosseini, K.; Ilie, M.; Mirzazade, M.; Baleanu, Dumitru; 56389
The present article aims to present a comprehensive study on a nonlinear time-fractional model involving the Caputo-Fabrizio (CF) derivative. More explicitly, a new (2+1)-dimensional mKdV (2D-mKdV) equation involving the Caputo-Fabrizio time-fractional derivative is considered and an analytic approximation for it is retrieved through a systematic technique, called the homotopy analysis transform (HAT) method. Furthermore, after proving the Lipschitz condition for the kernel psi (x,y,t;u), the fixed-point theorem is formally utilized to demonstrate the existence and uniqueness of the solution of the new 2D-mKdV equation involving the CF time-fractional derivative. A detailed study finally is carried out to examine the effect of the Caputo-Fabrizio operator on the dynamics of the obtained analytic approximation.
Citation Count: Khoshkenar, A. (2022). "Further studies on ordinary differential equations involving the M-fractional derivative", AIMS Mathematics, Vol.7, No.6, pp.10977-10993.
Further studies on ordinary differential equations involving the M-fractional derivative
(2022) Khoshkenar, A.; Ilie, M.; Hosseini, K.; Baleanu, D.; Salahshour, S.; Park, C.; Lee, J.R.; 56389
In the current paper, the power series based on the M-fractional derivative is formally introduced. More peciesely, the Taylor and Maclaurin expansions are generalized for fractional-order differentiable functions in accordance with the M-fractional derivative. Some new definitions, theorems, and corollaries regarding the power series in the M sense are presented and formally proved. Several ordinary differential equations (ODEs) involving the M-fractional derivative are solved to examine the validity of the results presented in the current study.