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Solving A Class Of Ordinary Differential Equations And Fractional Differential Equations With Conformable Derivative By Fractional Laplace Transform, Mohammad Molaei, Farhad Dastmalchi Saei, Mohammad Javidi, Yaghoub Mahmoudi
Solving A Class Of Ordinary Differential Equations And Fractional Differential Equations With Conformable Derivative By Fractional Laplace Transform, Mohammad Molaei, Farhad Dastmalchi Saei, Mohammad Javidi, Yaghoub Mahmoudi
Turkish Journal of Mathematics
In this paper, we use the fractional Laplace transform to solve a class of second-order ordinary differential equations (ODEs), as well as some conformable fractional differential equations (CFDEs), including the Laguerre conformable fractional differential equation. Specifically, we apply the transform to convert the differential equations into first-order, linear differential equations. This is done by using the fractional Laplace transform of order $\alpha+\beta$ or $\alpha+\beta+\gamma$. Also, we investigate some more results on the fractional Laplace transform, obtained by Abdeljawad.
Infinitely Many Positive Solutions For An Iterative System Of Conformable Fractional Order Dynamic Boundary Value Problems On Time Scales, Mahammad Khuddush, Kapula Rajendra Prasad
Infinitely Many Positive Solutions For An Iterative System Of Conformable Fractional Order Dynamic Boundary Value Problems On Time Scales, Mahammad Khuddush, Kapula Rajendra Prasad
Turkish Journal of Mathematics
In this paper, we establish infinitely many positive solutions for the iterative system of conformable fractional order dynamic equations on time scales $$ \begin{aligned} &\mathcal{T}_α^{\Delta}\big[\mathcal{T}_β^{\Delta}\big(\vartheta_\mathtt{n}(t)\big)\big]=\varphi(t)\mathtt{f}_\mathtt{n}\left(\vartheta_{\mathtt{n}+1}(t)\right),~t\in(0,1)_\mathbb{T},~1