DIFFERENTIAL EQUATIONS WITH TEMPERED Ψ-CAPUTO FRACTIONAL DERIVATIVE
Copyright policy )DIFFERENTIAL EQUATIONS WITH TEMPERED Ψ-CAPUTO FRACTIONAL DERIVATIVE
In this paper we define a new type of the fractional derivative, which we call tempered Ψ−Caputo fractional derivative. It is a generalization of the tempered Caputo fractional derivative and of the Ψ−Caputo fractional derivative. The Cauchy problem for fractional differential equations with this type of derivative is discussed and some existence and uniqueness results are proved. We present a Henry-Gronwall type inequality for an integral inequality with the tempered Ψ−fractional integral. This inequality is applied in the proof of an existence theorem. A result on a representation of solutions of linear systems of Ψ−Caputo fractional differential equations is proved and in the last section an example is presented.
- Comenius University Slovakia
Fractional ordinary differential equations, tempered Ψ−Caputo fractional derivative, Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations, Nonlinear ordinary differential equations and systems, Asymptotic properties of solutions to ordinary differential equations, tempered riemann-liouville fractional derivative, tempered \(\Psi\)-Caputo fractional derivative, tempered ψ−caputo fractional derivative, tempered Riemann-Liouville fractional derivative, QA1-939, Differential inequalities involving functions of a single real variable, Mathematics
Fractional ordinary differential equations, tempered Ψ−Caputo fractional derivative, Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations, Nonlinear ordinary differential equations and systems, Asymptotic properties of solutions to ordinary differential equations, tempered riemann-liouville fractional derivative, tempered \(\Psi\)-Caputo fractional derivative, tempered ψ−caputo fractional derivative, tempered Riemann-Liouville fractional derivative, QA1-939, Differential inequalities involving functions of a single real variable, Mathematics
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