On the Solutions of Fractional Cauchy Problem Featuring Conformable Derivative
Open Access
- 17 October 2018
- journal article
- research article
- Published by EDP Sciences in ITM Web of Conferences
- Vol. 22, 01045
- https://doi.org/10.1051/itmconf/20182201045
Abstract
In this study, we have obtained analytical solutions of fractional Cauchy problem by using q-Homotopy Analysis Method (q-HAM) featuring conformable derivative. We have considered different situations according to the homogeneity and linearity of the fractional Cauchy differential equation. A detailed analysis of the results obtained in the study has been reported. According to the results, we have found out that our obtained solutions approach very speedily to the exact solutions.Keywords
This publication has 22 references indexed in Scilit:
- Conformable heat equation on a radial symmetric plateThermal Science, 2017
- New properties of conformable derivativeOpen Mathematics, 2015
- Active Control of a Chaotic Fractional Order Economic SystemEntropy, 2015
- On the analytical solution of Fornberg–Whitham equation with the new fractional derivativePramana, 2015
- On conformable fractional calculusJournal of Computational and Applied Mathematics, 2015
- A new definition of fractional derivativeJournal of Computational and Applied Mathematics, 2014
- The homotopy analysis method for solving the time-fractional Fornberg–Whitham equation and comparison with Adomian’s decomposition methodApplied Mathematical Modelling, 2013
- The Analytical Solution of Some Fractional Ordinary Differential Equations by the Sumudu Transform MethodAbstract and Applied Analysis, 2013
- Approximate solutions to fractional subdiffusion equationsThe European Physical Journal Special Topics, 2011
- An approximate solution technique not depending on small parameters: A special exampleInternational Journal of Non-Linear Mechanics, 1995