Approximate Solution of the Fuzzy Triangular Initial Value Problem with Different Fractional Operator
Moath Ali Alshorman1, Nurnadiah Zamri2, Asia Khalaf Albzeirat3, Mohammed Ali4
1Moath Ali Alshorman, Faculty of Informatics and Computing, University Sultan Zainal Abidin, Besut Campus, Besut, Terengganu, Malaysia.
2Nurnadiah Zamri, Faculty of Informatics and Computing, University Sultan Zainal Abidin, Besut Campus, Besut, Terengganu, Malaysia.
3Asia Khalaf Albzeirat Department of Mathematics, Mutah University, Mutah, Jordan.
4Mohammed Ali Department of Mathematics, Jordan University of Science and Technology, Irbid, Jordan.
Manuscript received on April 02, 2020. | Revised Manuscript received on April 21, 2020. | Manuscript published on May 30, 2020. | PP: 1242-1249 | Volume-9 Issue-1, May 2020. | Retrieval Number: E6215018520/2020©BEIESP | DOI: 10.35940/ijrte.E6215.059120
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© The Authors. Blue Eyes Intelligence Engineering and Sciences Publication (BEIESP). This is an open access article under the CC-BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/)
Abstract: This study aims to conduct a comparison regarding the process of solving the fuzzy triangular initial value problem (FTIVP). The series solution of this problem is acquired through the reproducing kernel theory (RKT), although there have been past studies on FTIVP, there is no specialist study to compare solutions for the definition of different fractional operator. The comparisons where located through the difference in the use of an operator in the process of solution by using Riemann-Liouville integral operator (RLIO) and then by using Caputo fractional derivative operator (CFDO). Algorithm was presented to validate the method of solution and to view the effect of changing the operators on the solution behaviour in the two cases. During this comparison, the effectiveness of RKT was cleared and the notion of difference between using RLIO and CFDO were fixedly identified. Applications: The results identified in this research pronounced active difference in the behavior of errors, CDFO variations, and the behavior of error in favour of RLIO.
Keywords: Fuzzy Triangular Initial Value Problem, Riemann-Liouville Integral, Caputo Fractional Derivative, Reproducing Kernel Theory.
Scope of the Article: Fuzzy Logics