Browsing by Author "Chatzarakis, G.E."

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On the Qualitative Analysis of Solutions of Two Fractional Order Fractional Differential Equations
(Multidisciplinary Digital Publishing Institute (MDPI), 2024) Bolat, Y.; Gevgeşoğlu, M.; Chatzarakis, G.E.
In applied sciences, besides the importance of obtaining the analytical solutions of differential equations with constant coefficients, the qualitative analysis of the solutions of such equations is also very important. Due to this importance, in this study, a qualitative analysis of the solutions of a delayed and constant coefficient fractal differential equation with more than one fractional derivative was performed. In the equation under consideration, the derivatives are the Riemann–Liouville fractional derivatives. In the proof of the obtained results, Laplace transform formulas of the Riemann–Liouville fractional derivative and some inequalities are used. We also provide some examples to check the accuracy of our results.
On the Qualitative Analysis of Solutions of Two Fractional Order Fractional Differential Equations
(2024.01.01) Bolat, Y.; Gevgesoglu, M.; Chatzarakis, G.E.
In applied sciences, besides the importance of obtaining the analytical solutions of differential equations with constant coefficients, the qualitative analysis of the solutions of such equations is also very important. Due to this importance, in this study, a qualitative analysis of the solutions of a delayed and constant coefficient fractal differential equation with more than one fractional derivative was performed. In the equation under consideration, the derivatives are the Riemann-Liouville fractional derivatives. In the proof of the obtained results, Laplace transform formulas of the Riemann-Liouville fractional derivative and some inequalities are used. We also provide some examples to check the accuracy of our results.
Oscillatory properties for Emden-Fowler type difference equations with oscillating coefficients
(2024.01.01) Bolat, Y.; Gevgesoglu, M.; Chatzarakis, G.E.
In this paper, we give new criteria on the oscillation of the fourth-order Emden-Fowler type delay difference equation with oscillating coefficients of the form = 0, >= 0 , where = ( 3 ) and = + - . For this we use the Riccati transformation method and the comparison method. Also we give some examples to illustrate our results.
Oscillatory properties for Emden–Fowler type difference equations with oscillating coefficients
(Elsevier B.V., 2024) Bolat, Y.; Gevgeşoğlu, M.; Chatzarakis, G.E.
In this paper, we give new criteria on the oscillation of the fourth-order Emden–Fowler type delay difference equation with oscillating coefficients of the form ΔWn+rnyn−τβ=0,n≥n0,where Wn=pnΔ3vnα and vn=yn+qnyn−σ. For this we use the Riccati transformation method and the comparison method. Also we give some examples to illustrate our results.