Cauchy problems for fractional differential equations with Riemann–Liouville fractional derivatives
Copyright policy )Cauchy problems for fractional differential equations with Riemann–Liouville fractional derivatives
In this paper, the authors study certain Cauchy-type problems of fractional differential equations with fractional differential conditions, involving Riemann-Liouville derivatives, in infinite-dimensional Banach spaces. They introduce a certain fractional resolvent and study some of its properties. Moreover, they prove that a homogeneous \(\alpha\)-order Cauchy problem is well posed if and only if its coefficient operator is the generator of an \(\alpha\)-order fractional resolvent, and they give sufficient conditions to guarantee the existence and uniqueness of weak solutions and strong solutions of a certain inhomogeneous \(\alpha\)-order Cauchy problem.
- Xi’an Jiaotong-Liverpool University China (People's Republic of)
- Xi'an Jiaotong University China (People's Republic of)
Cauchy problem, Fractional resolvent, One-parameter semigroups and linear evolution equations, Riemann-Liouville fractional derivative, Fractional ordinary differential equations, Fractional partial differential equations, fractional resolvent, Well-posedness, Fractional derivatives and integrals, well-posedness, Riemann–Liouville fractional derivative, Analysis
Cauchy problem, Fractional resolvent, One-parameter semigroups and linear evolution equations, Riemann-Liouville fractional derivative, Fractional ordinary differential equations, Fractional partial differential equations, fractional resolvent, Well-posedness, Fractional derivatives and integrals, well-posedness, Riemann–Liouville fractional derivative, Analysis
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