Original scientific paper https://doi.org/10.2298/TSCI170624266BThe aim of this work is to determine an approximate solution of a fractional order Volterra-Fredholm integro-differential equation using by the Sinc-collocation method. Conformable derivative is considered for the fractional derivatives. Some numerical examples having exact solutions are approximately solved. The comparisons of the exact and the approximate solutions of the examples are presented both in tables and graphical forms.

In this work, we aim to determine the possible soliton solutions and examine the behaviors of the (1+1)-dimensional non-linear Telegraph equation (NTE) which is used to model signal processing for the propagation of transmission of the electric impulses and also wave theory process by using the extended Kudryashov method. We started by finding the non-linear ordinary differential form of the (1+1)-NTE with the aid of a suitable wave transformation. Then, the extended Kudryashov method approach has been demonstrated and implemented to the obtained non-linear ordinary differential form. As a result, a polynomial expression has been achieved and converted to a linear algebraic equation system. Soliton solutions of the investigated equation are produced by solving the system and choosing the appropriate solution sets. Finally, graphical depictions, gained results and necessary comments are given.

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Bu çalışmada, farklı sınır koşulları için kesirli mertebeden bir diferansiyel denklem sınıfını ele aldık. Bu kesirli mertebeden sınır değer problemlerinin(KSDP) yaklaşık çözümlerini elde etmek için Sinc Sıralama Yöntemi (SSY) uygulanmıştır. Kesirli türevler için Beta türevi alınmıştır. Ayrıca, bir takım test örnekleri sayısal simulasyonlarla birlikte verilmiştir. Yakınsaklık analizi SSY 'nin tutarlı ve etkin bir yöntem olduğunu göstermiştir.

Abstract:The Fractional Boundary Value Problems (BVPs) oftenly come across in the modelling of several problems that we are faced in the branches of engineering sciences. The main aim of this work is to compute the solution of the Fractional BVP which is formed bywith the boundary conditions y(a) = 0, y(b) = 0 approximately by using the Sinc-Galerkin Method. Conformable sense is considered for the fractional derivatives. Intercalarity, some test problems having exact solutions are approximately solved. Afterwards, the exact solutions compared with the approximate solutions and numerical results of that comparison are presented both in table and graphical forms.