New Results Achieved for Fractional Differential Equations with Riemann–Liouville Derivatives of Nonlinear Variable Order

Date
2023-09-20
Authors
Abdelhamid, Hallouz
Stamov, Gani
Souid, Mohammed Said
Stamova, Ivanka
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Journal ISSN
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Abstract

This paper proposes new existence and uniqueness results for an initial value problem (IVP) of fractional differential equations of nonlinear variable order. Riemann–Liouville-type fractional derivatives are considered in the problem. The new fundamental results achieved in this work are obtained by using the inequalities technique and the fixed point theory. In addition, uniform stability criteria for the solutions are derived. The accomplished results are new and complement the scientific research in the field. A numerical example is composed to show the efficacy and potency of the proposed criteria.

Description
Keywords
fractional derivatives and integrals of variable order, fixed point theorem, initial value problem, uniform stability
Citation
Axioms 12 (9): 895 (2023)
Department
Mathematics