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    Analytical Results of Morphochemical Electrodeposition Model
    (Springer, 2020) Pinar, Zehra
    Mathematical modeling of electrochemical dynamics and related patterning processes was developed primarily for variants of the activator-inhibitor mechanism and focused more on electro-catalysis than electrodeposition. In addition, these phenomena are expressed mathematically generally by the reaction–diffusion model, instead artificially, it is the evaluation of reactive species as state concentrations as state variables for electrodeposition models. For the considered models, the exact solutions in the explicit form were not obtained literature to our knowledge. Our main aim is to fill this gap by revealing their exact solutions. Finally, the obtained results confirm that the considered solution procedure can be widely employed to find the solution and also capture some interesting and simulating consequences. © 2020, Shiraz University.
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    An Analytical Studies of the Reaction- Diffusion Systems of Chemical Reactions
    (Springer, 2021) Pinar, Zehra
    Reaction–diffusion systems are seen in not only many fields of science but also social behaviorus. In this work, Schnakenberg, Brusselator and Lengyel–Epstein models are considered that are the best known the chemical reaction–diffusion models and are also seen in a large scale of applications in biological or biochemical processes. Due to its importance in science and applications, for the considered models, till now the numerical and approximate solutions are obtained whereas the exact solutions in the explicit form were not obtained literature to our knowledge. Our main aim is to fill this gap by revealing their exact solutions. To obtain the exact solutions, the ansatz-based methods are considered in a novel way. The obtained results have a major role in the literature so that the considered models are seen in a large scale of applications not only chemical but also biological or biochemical processes. © 2021, The Author(s), under exclusive licence to Springer Nature India Private Limited.
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    The Combination of Conservation Laws and Auxiliary Equation Method
    (Springer, 2020) Pinar, Zehra
    In this paper, appropriate Lie group transformations are considered as an alternative to a travelling wave transformation, in the auxiliary equation method to solve the nonlinear partial differential equations. In addition, Bernoulli differential equation has been considered as an auxiliary equation and using the approach presented. © 2019, Springer Nature India Private Limited.
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    On the explicit solutions of fractional Bagley-Torvik equation arises in engineering
    (Balikesir University, 2019) Pinar, Zehra
    In this work, Bagley-Torvik equation is considered with conformable derivatives. The analytical solutions will be obtained via Sine-Gordon expansion method and Bernouli equation method for the two cases of Bagley-Torvik equation. We will illustrate and discuss about the methodology and solutions therefore the proposed equation has meaning in different areas of science and engineering. © 2019 Balikesir University. All rights reserved.
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    On the Hermite and Mathieu Special Characterizations to the Logarithmic Zakharov–Kuznetsov Equations
    (Springer, 2024) Pinar, Zehra; Baskonus, Haci Mehmet; Veeresha, P.; Gao, Wei
    In this paper, we find the new travelling wave solutions for several aspects of logarithmic Zakharov–Kuznetsov (ZK) equations using an efficient technique called the special function method which is composed of Hermite and Mathieu differential equations being novel and special functions. In order to illustrate the efficiency of the projected scheme, we considered four different examples with different cases, namely, logarithmic ZK (log-ZK) equation, logarithmic modified ZK (log-mZK) equation, and logarithmic ZK modified equal width (log-ZK-mEW) equation and logarithmic ZK–Benjamin–Bona–Mahony (log-ZKBBM) equation. The behaviour of the obtained results and corresponding consequences are illustrated and captured. Finally, the obtained results confirm that the considered solution procedure can be widely employed to find the solution and also capture some interesting and stimulating consequences. © 2023, The Author(s), under exclusive licence to Springer Nature India Private Limited.
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    Semi-Analytical Solutions of Batch System Population Balance Models
    (Chiang Mai University, 2022) Pinar, Zehra
    We propose a semi-analytical method to solve partial integro-differential equations with ini-tial/boundary conditions. This work investigates the semi-analytical solutions of the population balance models (PBMs) for the batch systems. The comparison of obtained solutions with the known exact solutions is given to show the effectiveness of the proposed method. The proposed method is very useful, reliable, and flexible; also, the solutions can play key role population balance models in engineering and science which are different kinds of partial integro-differential equations. © 2022 by TJM. All rights reserved.