On the Existence and Stability of Solutions for a Class of Fractional Riemann–Liouville Initial Value Problems

Luís P. Castro () and Anabela S. Silva
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Luís P. Castro: CIDMA—Center for Research and Development in Mathematics and Applications, University of Aveiro, 3810-193 Aveiro, Portugal
Anabela S. Silva: CIDMA—Center for Research and Development in Mathematics and Applications, University of Aveiro, 3810-193 Aveiro, Portugal

Mathematics, 2023, vol. 11, issue 2, 1-22

Abstract: This article deals with a class of nonlinear fractional differential equations, with initial conditions, involving the Riemann–Liouville fractional derivative of order α ∈ ( 1 , 2 ) . The main objectives are to obtain conditions for the existence and uniqueness of solutions (within appropriate spaces), and to analyze the stabilities of Ulam–Hyers and Ulam–Hyers–Rassias types. In fact, different conditions for the existence and uniqueness of solutions are obtained based on the analysis of an associated class of fractional integral equations and distinct fixed-point arguments. Additionally, using a Bielecki-type metric and some additional contractive arguments, conditions are also obtained to guarantee Ulam–Hyers and Ulam–Hyers–Rassias stabilities for the problems under analysis. Examples are also included to illustrate the theory.

Keywords: fractional differential equations; Riemann–Liouville derivative; fixed point theory; Ulam–Hyers stability; Ulam–Hyers–Rassias stability (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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