Scopus İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651
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Article Citation - WoS: 86Citation - Scopus: 97On Fractional Derivatives With Generalized Mittag-Leffler Kernels(Pushpa Publishing House, 2018) Abdeljawad, Thabet; Baleanu, DumitruFractional derivatives with three parameter generalized Mittag-Leffler kernels and their properties are studied. The corresponding integral operators are obtained with the help of Laplace transforms. The action of the presented fractional integrals on the Caputo and Riemann type derivatives with three parameter Mittag-Leffler kernels is analyzed. Integration by parts formulas in the sense of Riemann and Caputo are proved and then used to formulate the fractional Euler-Lagrange equations with an illustrative example. Certain nonconstant functions whose fractional derivatives are zero are determined as well.Article Citation - WoS: 113Citation - Scopus: 120The New Exact Solitary Wave Solutions and Stability Analysis for the (2+1)-Dimensional Zakharov-Kuznetsov Equation(Pushpa Publishing House, 2019) Yusuf, Abdullahi; Inc, Mustafa; Baleanu, Dumitru; Ghanbari, BehzadIn this paper, a new generalized exponential rational function method is employed to extract new solitary wave solutions for the Zakharov-Kuznetsov equation (ZKE). The ZKE exhibits the behavior of weakly nonlinear ion-acoustic waves in incorporated hot isothermal electrons and cold ions in the presence of a uniform magnetic field. Furthermore, the stability for the governing equations is investigated via the aspect of linear stability analysis. Numerical simulations are made to shed light on the characteristics of the obtained solutions.Article Citation - WoS: 40Citation - Scopus: 46The Mean Value Theorem and Taylor's Theorem for Fractional Derivatives With Mittag-Leffler Kernel(Pushpa Publishing House, 2018) Baleanu, Dumitru; Fernandez, ArranWe establish analogues of the mean value theorem and Taylor's theorem for fractional differential operators defined using a Mittag-Leffler kernel. We formulate a new model for the fractional Boussinesq equation by using this new Taylor series expansion.Article Citation - WoS: 8Citation - Scopus: 12On Neutral Impulsive Stochastic Differential Equations With Poisson Jumps(Pushpa Publishing House, 2018) Kandasamy, Banupriya; Baleanu, Dumitru; Arumugam, Vinodkumar; Annamalai, Anguraj; Vinodkumar, ArumugamWe study the results of existence and continuous dependence on neutral impulsive stochastic differential equations with Poisson jumps. We have also created some conditions confirming exponential stability.Article Citation - WoS: 22Citation - Scopus: 29Solution of Fractional Differential Equations Via Α - Ψ-Geraghty Type Mappings(Pushpa Publishing House, 2018) Kalantari, Sabileh; Baleanu, Dumitru; Afshari, HojjatUsing fixed point results of alpha - psi-Geraghty contractive type mappings, we examine the existence of solutions for some fractional differential equations in b-metric spaces. By some concrete examples we illustrate the obtained results.Article Citation - WoS: 11Citation - Scopus: 17Local Existence for an Impulsive Fractional Neutral Integro-Differential System With Riemann-Liouville Fractional Derivatives in a Banach Space(Pushpa Publishing House, 2018) Baleanu, Dumitru; Arjunan, Mani Mallika; Kalamani, Palaniyappan; Mallika Arjunan, ManiIn this manuscript, we investigate a sort of fractional neutral integro-differential equations with impulsive outcomes and extend the formula of general solutions for the impulsive fractional neutral integro-differential system in a Banach space. By using the analysis of the limit case and the operator generating compact semigroup, we derive the main results. Finally, an example is discussed to illustrate the efficiency of the results.Article Citation - WoS: 24Citation - Scopus: 31New Dual-Mode Kadomtsev-Petviashvili Model With Strong-Weak Surface Tension: Analysis and Application(Pushpa Publishing House, 2018) Alquran, Marwan; Jaradat, Imad; Baleanu, Dumitru; Abu Irwaq, IssamDual-mode (2 + 1)-dimensional Kadomtsev-Petviashvili (DMKP) equation is a new model which represents the spread of two simultaneously directional waves due to the involved term " utt (x, y, t)" in its equation. We present the construction of DMKP and search for possible solutions. The innovative tanh-expansion method and Kudryashov technique will be utilized to find the necessary constraint conditions which guarantee the existence of soliton solutions to DMKP. Supportive 3D plots will be provided to validate our findings.Article On fractional derivatives with generalized Mittag-Leffler kernels(Pushpa Publishing House, 2018) Abdeljawad, Thabet; Baleanu, DumitruFractional derivatives with three parameter generalized Mittag-Leffler kernels and their properties are studied. The corresponding integral operators are obtained with the help of Laplace transforms. The action of the presented fractional integrals on the Caputo and Riemann type derivatives with three parameter Mittag-Leffler kernels is analyzed. Integration by parts formulas in the sense of Riemann and Caputo are proved and then used to formulate the fractional Euler-Lagrange equations with an illustrative example. Certain nonconstant functions whose fractional derivatives are zero are determined as well.