Trapezoidal Scheme for the Numerical Solution of Fractional Initial Value Problems
(1) * Iqbal M. Batiha Mail (1) Department of Mathematics, Al Zaytoonah University of Jordan, Amman 11733, Jordan. 2) Nonlinear Dynamics Research Center (NDRC), Ajman University, Ajman 346, United Arab Emirates)
(2) Hebah F. Alsamad Mail (Al Zaytoonah University of Jordan, Jordan)
(3) Iqbal H. Jebril Mail (Al Zaytoonah University of Jordan, Jordan)
(4) Hamzah O. Al-Khawaldeh Mail (Al Al-Bayt University, Jordan)
(5) Wala’a A. Al Kasasbeh Mail (Al Zaytoonah University of Jordan, Jordan)
(6) Shaher Momani Mail (1) Nonlinear Dynamics Research Center (NDRC), Ajman University, Ajman 346, United Arab Emirates. 2) Department of Mathematics, University of Jordan, Amman, Jordan)
*corresponding author

Abstract


The purpose of this study is to recall the main concepts and definitions in relation to the fractional calculus. In light of this overview, we will propose a novel fractional version of the so-called Trapezoid method named by the fractional Trapezoid method. Such a method will then be used to numerically solve the analog version of the initial value problems called fractional initial value problem FIVPs. As consequences of the proposed numerical approach, several numerical examples will be illustrated to verify the efficiency of the proposed numerical approach.


Keywords


Fractional Calculus; Fractional Initial Value Problem; Fractional Taylor Formula; Fractional Trapezoid Method

   

DOI

https://doi.org/10.31763/ijrcs.v5i2.1795 		      

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