On the Qualitative Analysis of Solutions of Two Fractional Order Fractional Differential Equations

Yasar Bolat, Murat Gevgeşoğlu and George E. Chatzarakis ()
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Yasar Bolat: Department of Mathematics, Faculty of Arts & Sciences, Kastamonu University, Kastamonu 37210, Turkey
Murat Gevgeşoğlu: Department of Mathematics, Faculty of Arts & Sciences, Kastamonu University, Kastamonu 37210, Turkey
George E. Chatzarakis: Department of Electrical and Electronic Engineering Educators, School of Pedagogical & Technological Education, 15122 Marousi, Greece

Mathematics, 2024, vol. 12, issue 16, 1-7

Abstract: In applied sciences, besides the importance of obtaining the analytical solutions of differential equations with constant coefficients, the qualitative analysis of the solutions of such equations is also very important. Due to this importance, in this study, a qualitative analysis of the solutions of a delayed and constant coefficient fractal differential equation with more than one fractional derivative was performed. In the equation under consideration, the derivatives are the Riemann–Liouville fractional derivatives. In the proof of the obtained results, Laplace transform formulas of the Riemann–Liouville fractional derivative and some inequalities are used. We also provide some examples to check the accuracy of our results.

Keywords: fractional derivative; fractional-order differential equations; qualitative analysis; oscillatory behavior (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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