Matematik Bölümü Yayın Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/413
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Article YFICITIOUS TIME INTEGRATION METHOD FOR SOLVING THE TIME FRACTIONAL GAS DYNAMICS EQUATION(2019) Partohaghighi, Mohammad; İnç, Mustafa; Baleanu, Dumitru; Moshokoa, Seithuti PhilemonIn this work a poweful approach is presented to solve the time-fractional gas dynamics equation. In fact, we use a fictitious time variable y to convert the dependent variable w(x, t) into a new one with one more dimension. Then by taking a initial guess and implementing the group preserving scheme we solve the problem. Finally four examples are solved to illustrate the power of the offered method.Article ON THE INTERPOLATIVE (phi, psi)-TYPE Z-CONTRACTION(2021) Khan, Mohammad S.; Singh, Y. Mahendra; Karapınar, ErdalIn this paper, we introduce the notions of interpolative (phi, psi)-type Z-contraction with respect to simulation function and quasi triangular theta-orbital admissible mapping. Using these notions, some fixed point theorems are also established in the framework of metric space. An illustrative example is furnished to show that there exists a quasi triangular theta-orbital admissible mapping which is not a triangular theta-admissible. As an application of our result, we establish an existence of solution for a non-linear Fredholm integral equation.Article Dynamics of optical solitons, multipliers and conservation laws to the nonlinear schrodinger equation in (2+1)-dimensions with non-Kerr law nonlinearity(2019) Aliyu, Aliyu Isa; Tchier, Fairouz; İnç, Mustafa; Yusuf, Abdullah; Baleanu, DumitruThis work studies the (2 + 1)-dimensional nonlinear Schrodinger equation which arises in optical fibre. Grey and black optical solitons of the model are reported using a suitable complex envelope ansatz solution. The integration lead to some certain conditions which must be satisfied for the solitons to exist. On applying the Chupin Liu's theorem to the grey and black optical solitons, we construct new sets of combined optical soliton solutions of the model. Moreover, classification of conservation laws (Cls) of the model is implemented using the multipliers approach. This is achieved by constructing a set of first-order multipliers of a system of nonlinear partial differential equations acquired by transforming the model into real and imaginary components are derived, which are subsequently used to construct the Cls.Article Convolution theorems associated with some integral operators and convolutions(Taylor&Francis LTD, 2019) Al-Omari, Shrideh Khalaf Qasem; Baleanu, Dumitru; Ata, Yalcin; Baykal, YahyaIn this article, various convolution theorems involving certain weight functions and convolution products are derived. The convolution theorems we obtain are more general, convenient, and efficient than the complicated convolution theorem of the Hartley transform. Further results involving new variants of generalizations of Fourier and Hartley transforms are also discussed.