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    Approximate solutions of the time-fractional Kadomtsev-Petviashvili equation with conformable derivative
    (Erzincan Üniversitesi, 2019) Durur, Hülya; Şenol, Mehmet; Kurt, Ali; Taşbozan, Orkun
    In this study, residual power series method, namely RPSM, is applied to solve time-fractional KadomtsevPetviashvili (K-P) differential equation. In the solution procedure, the fractional derivatives are explained in the conformable sense. The model is solved approximately and the obtained results are compared with exact solutions obtained by the sub-equation method. The results reveal that the present method is accurate, dependable, simple to apply and a good alternative for seeking solutions of nonlinear fractional partial differential equations.
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    The exact solutions of conformable fractional partial differential Equations using new sub equation method
    (Fuat USTA, 2019) Kurt, Ali; Taşbozan, Orkun; Durur, Hülya
    In this article, authors employed the new sub equation method to attain new traveling wave solutions of conformable time fractional partial differential equations. Conformable fractional derivative is a well behaved, applicable and understandable definition of arbitrary order derivation. Also this derivative obeys the basic properties that Newtonian concept satisfies. In this study authors obtained the exact solution for KDV equation where the fractional derivative is in conformable sense. New solutions are obtained in terms of the generalized version of the trigonometric functions.
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    The New Travelling Wave Solutions of Time Fractional Fitzhugh-Nagumo Equation with Sine-Gordon Expansion Method
    (Adiyaman University, 2020) Taşbozan, Orkun; Kurt, Ali
    Authors aimed to employ the sine-Gordon expansion method to acquire the new exact solutions of fractional Fitzhugh-Nagumo equation which is a stripped type of the Hodgkin-Huxley model that expresses in extensive way activation and deactivation dynamics of neuron spiking. By using the wave transformations, by the practicality of chain rule and applicability of the conformable fractional derivative, the fractional nonlinear partial differential equation (FNPDE) changes to a nonlinear ordinary differential equation. So the exact solution of the considered equation can be obtained correctly with the aid of efficient and reliable analytical techniques. © 2020, Adiyaman University. All rights reserved.
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    Yardımcı denklem yöntemi yardımı ile kesirli mertebeden kısmi diferansiyel denklemlerinin analitik çözümleri
    (Afyon Kocatepe Üniversitesi, 2019) Yılmaz, Sera; Taşbozan, Orkun
    Bu makalede conformable kesirli mertebeden türev içeren lineer olmayan kesirli mertebeden Konopelchenko-Dubrovsky ve Benjamin-Ono denklemlerinin analitik çözümleri yardımcı denklem yöntemi ile elde edildi. Her iki denklem dalga dönüşümü yardımıyla lineer olmayan adi türevli diferansiyel denkleme dönüştürüldükten sonra yardımcı denklem yöntemi kullanıldı. Elde edilen çözümlerin üç boyutlu grafikleri verildi. Yardımcı denklem yöntemi, diğer analitik yöntemlere göre daha çok analitik çözüm içermektedir.