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Öğe An approximate solution of fractional cable equation by homotopy analysis method(SpringerOpen, 2014-03-16) İnç, Mustafa; Cavlak, Ebru; Bayram, MustafaIn this article, the homotopy analysis method (HAM) is applied to solve the fractional cable equation by the Riemann-Liouville fractional partial derivative. This method includes an auxiliary parameter h which provides a convenient way of adjusting and controlling the convergence region of the series solution. In this study, approximate solutions of the fractional cable equation are obtained by HAM. We also give a convergence theorem for this equation. A suitable value for the auxiliary parameter h is determined and results obtained are presented by tables and figures.Öğe Dark-Bright Optical Soliton and Conserved Vectors to the Biswas-Arshed Equation With Third-Order Dispersions in the Absence of Self-Phase Modulation(FRONTIERS MEDIA SA, AVENUE DU TRIBUNAL FEDERAL 34, LAUSANNE, CH-1015, SWITZERLAND, 2019) Aliyu, Aliyu Ise; İnç, Mustafa; Yusuf, Abdullahi; Baleanu, Dumitru; Bayram, MustafaThe form-I version of the new celebrated Biswas-Arshed equation is studied in this work with the aid of complex envelope ansatz method. The equation is considered when self-phase is absent and velocity dispersion is negligibly small. New Dark-bright optical soliton solution of the equation emerge from the integration. The acquired solution combines the features of dark and bright solitons in one expression. The solution obtained are not yet reported in the literature. Moreover, we showed that the equation possess conservation laws (Cls).Öğe Invariant subspaces, exact solutions and stability analysis of nonlinear water wave equations(ELSEVIER, RADARWEG 29, 1043 NX AMSTERDAM, NETHERLANDS, 2020) Hosseini, Kamyar; İnç, Mustafa; Shafiee, Mahmoud; Ilie, Mousa; Shafaroody, A.; Yusuf, Abdelrhman; Bayram, MustafaThe key purpose of the present research is to derive the exact solutions of nonlinear water wave equations (NLWWEs) in oceans through the invariant subspace scheme (ISS). In this respect, the NLWWEs which describe specific nonlinear waves are converted to a number of systems of ordinary differential equations (ODEs) such that the resulting systems can be efficiently handled by computer algebra systems. As an accomplishment, the performance of the well-designed ISS in extracting a group of exact solutions is formally confirmed. In the end, the stability analysis for the NLWWE is investigated through the linear stability scheme.Öğe New optical solitons for Biswas-Arshed equation with higher order dispersions and full nonlinearity(ELSEVIER GMBH, HACKERBRUCKE 6, 80335 MUNICH, GERMANY, 2020) Körpınar, Zeliha; İnç, Mustafa; Bayram, Mustafa; Hashemi, Mir SajjadIn this paper, the extended Jacobi's elliptic function approach is used to solve the Biswas–Arshed equation in two different types. This method reveals several optical solitons including traveling wave solutions. The found solutions are identified bright, dark, singular optical solitons and Jacobi elliptic function solutions. Reliability of the process is presented with graphical consequence of derived solutions.Öğe New Soliton Solutions of the Fractional Regularized Long Wave Burger Equation by Means of Conformable Derivative(ELSEVIER, RADARWEG 29, 1043 NX AMSTERDAM, NETHERLANDS, 2019) Körpınar, Zeliha; Tchier, Fairouz; İnç, Mustafa; Ragoub, Lakhdar; Bayram, MustafaIn this paper, the practice of the extended direct algebraic method (EDAM) is used to solve fractional Regularized Long Wave Burgers (RLW-Burgers) equation by means of the conformable derivative. Firstly, this fractional equation is changed into the ordinary differential equation by using the traveling wave transformation. Then new soliton solutions are obtained by using EDAM. This presented form is important in physics and engineering. The created soliton solutions play a major task for scientists about an agreement the physical event of this equation. The graphics of some solutions are drawn at fitting values of parameters. The obtained outcomes appear clarity, accuracy, and potentiality of the presented scheme.Öğe New Solutions of the Fractional Boussinesq-like Equations by Means of Conformable Derivatives(ELSEVIER SCIENCE BV, PO BOX 211, 1000 AE AMSTERDAM, NETHERLANDS, 2019) Körpınar, Zeliha; Tchier, Fairouz; İnç, Mustafa; Ragoub, Lakhdar; Bayram, MustafaIn this paper, the process of the extended direct algebraic method (EDAM) is used to solve two fractional Boussinesq-like equations by means of conformable derivatives. Firstly, these fractional equations are changed into the ordinary differential equations by using the traveling wave transformation. Then new solutions are obtained by using EDAM. This dynamical model plays a key role in engineering and physics. The constructed solitons solution help researchers in understanding the physical phenomenon of this equation. The standard linear stability analysis is utilized and the stability of the model is investigated which substantiate that all results are stable and exact. Graphically, the movements of some solutions are depicted at appropriate values of parameters. The achieved results show simplicity, reliability, and power of the current schemes.Öğe On numerical solution of the time-fractional diffusion-wave equation with the fictitious time integration method(SPRINGER HEIDELBERG, TIERGARTENSTRASSE 17, D-69121 HEIDELBERG, GERMANY, 2019) Hashemi, Mir Sajjad; İnç, Mustafa; Parto-Haghighi, Mohammad; Bayram, MustafaIn this work we offer a robust numerical algorithm based on the Lie group to solve the timefractional diffusion-wave (TFDW) equation. Firstly, we use a fictitious time variable ? to convert the related variable u(x, t) into a new space with one extra dimension. Then by using a composition of the group preserving scheme (GPS) and a semi-discretization of new variable, we approximate the solutions of the problem. Finally, various numerical experiments are performed to illustrate the power and accuracy of the given method.Öğe Soliton Solutions for Kudryashov-Sinelshchikov Equation(YILDIZ TECHNICAL UNIV, YILDIZ CAMPUS, BESIKTAS, ISTANBUL, 34349, TURKEY, 2019) Yusuf, Abdullahi; İnç, Mustafa; Bayram, MustafaThis paper acquires the closed form solutions for the Kudryashov-Sinelshchikov (KS) equation. The Riccati-Bernoulli (RB) sub-ODE method is used to acquire such solitons whose structure include trigonmetric, hyperbolic and algebraic structures. Some interesting figures for the obtained solutions are presented in order to shed light on the characteristics of the solutions.Öğe Symmetry Properties and Exact Solutions of the Time Fractional Kolmogorov-Petrovskii-Piskunov Equation(SOC MEXICANA FISICA, APARTADO POSTAL 70-348, COYOACAN 04511, MEXICO, 2019) Hashemi, Mir Sajjad; İnç, Mustafa; Bayram, MustafaIn this paper, the time fractional Kolmogorov-Petrovskii-Piskunov (TFKPP) equation is analyzed by means of Lie symmetry approach. The TFKPP is reduced to ordinary differential equation of fractional order via the attained point symmetries. Moreover, the simplest equation method is used in construct the exact solutions of underlying equation with recently introduced conformable fractional derivative.Öğe Theory and application for the system of fractional Burger equations with Mittag leffler kernel(ELSEVIER SCIENCE INC, STE 800, 230 PARK AVE, NEW YORK, NY 10169, 2020) Körpınar, Zeliha; İnç, Mustafa; Bayram, MustafaIn this work, the system of fractional Burger differential equations are presented as a new fractional model for Atangana–Baleanu fractional derivative with Mittag leffler kernel. The approximate consequences are analysed by applying an recurrent process. The existence and uniquenes of solution for this system is discussed. In order to appear the effects of several parameter and variables on the movement, the approximate results are showed in graphics and are compared with obtained solutions for two different derivative in tables.Öğe Theory and Application for the Time Fractional Gardner Equation with Mittag-Leffler Kernel(TAYLOR & FRANCIS LTD, 2-4 PARK SQUARE, MILTON PARK, ABINGDON OR14 4RN, OXON, ENGLAND, 2019) Körpınar, Zeliha; İnç, Mustafa; Baleanu, Dumitru; Bayram, MustafaIn this work, the time fractional Gardner equation is presented as a new fractional model for Atangana-Baleanu fractional derivative with Mittag-Leffler kernel. The approximate consequences are analysed by applying a recurrent process. The existence and uniqueness of solution for this system is discussed. To explain the effects of several parameters and variables on the movement, the approximate results are shown in graphics and tables.Öğe Two reliable methods for solving the forced convection in a porous-saturated duct(SPRINGER HEIDELBERG, TIERGARTENSTRASSE 17, D-69121 HEIDELBERG, GERMANY, 2020) Hashemi, Mir Sajjad; İnç, Mustafa; Seyfi, Negar; Bayram, MustafaIn this paper, the solution of nonlinear forced convection in a porous saturable duct is numerically approximated by two different approaches. The first one is a Lie group integrator based on the group SL2(R), whose calculation is far simpler and easier. The second method is reproducing kernel Hilbert space (RKHS) method which uses the Hilbert spaces in calculation. Convergence analyses for both methods were done. Effects of the porous media shaped parameter, Forchheimer number, and viscosity ratio on the solutions are discussed and illustrated by the proposed methods. The numerical experimentsshowed that the SL2(R)-shooting method and RKHS method are suitable for solving the forced convection in a porous-saturated duct with high accuracy and efficiency.
