Two Analytical Techniques for Fractional Differential Equations with Harmonic Terms via the Riemann–Liouville Definition

Ragwa S. E. Alatwi, Abdulrahman F. Aljohani, Abdelhalim Ebaid () and Hind K. Al-Jeaid ()
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Ragwa S. E. Alatwi: Computational & Analytical Mathematics and Their Applications Research Group, Department of Mathematics, Faculty of Science, University of Tabuk, Tabuk 71491, Saudi Arabia
Abdulrahman F. Aljohani: Computational & Analytical Mathematics and Their Applications Research Group, Department of Mathematics, Faculty of Science, University of Tabuk, Tabuk 71491, Saudi Arabia
Abdelhalim Ebaid: Computational & Analytical Mathematics and Their Applications Research Group, Department of Mathematics, Faculty of Science, University of Tabuk, Tabuk 71491, Saudi Arabia
Hind K. Al-Jeaid: Department of Mathematical Sciences, Umm Al-Qura University, Makkah 715, Saudi Arabia

Mathematics, 2022, vol. 10, issue 23, 1-11

Abstract: This paper considers a class of non-homogeneous fractional systems with harmonic terms by means of the Riemann–Liouville definition. Two different approaches are applied to obtain the dual solution of the studied class. The first approach uses the Laplace transform (LT) and the solution is given in terms of the Mittag-Leffler functions. The second approach avoids the LT and expresses the solution in terms of exponential and periodic functions which is analytic in the whole domain. The current methods determine the solution directly and efficiently. The results are applicable for other problems of higher order.

Keywords: periodic solution; Mittag-Leffler; Riemann–Liouville; fractional calculus; Laplace transform (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (1)

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