A Class of Quasilinear Equations with Riemann–Liouville Derivatives and Bounded Operators

Axioms

Mikhail M. Turov¹  Vladimir E. Fedorov¹  Bui Trong Kien² 

[1] Department of Mathematical Analysis, Mathematics Faculty, Chelyabinsk State University, Kashirin Brothers St., 129, 454001 Chelyabinsk, Russia;Department of Optimization and Control Theory, Institute of Mathematics of the Vietnam Academy of Sciences and Technologies, 8 Hoang Quoc Viet Road, Caugiay District, Hanoi 10307, Vietnam;

关键词: multi-term fractional differential equation;    quasilinear equation;    Riemann–Liouville fractional derivative;    defect of Cauchy type problem;    fixed point theorem;    initial-boundary value problem;   

DOI  :  10.3390/axioms11030096

来源: DOAJ

【 摘 要 】

The existence and uniqueness of a local solution is proved for the incomplete Cauchy type problem to multi-term quasilinear fractional differential equations in Banach spaces with Riemann–Liouville derivatives and bounded operators at them. Nonlinearity in the equation is assumed to be Lipschitz continuous and dependent on lower order fractional derivatives, which orders have the same fractional part as the order of the highest fractional derivative. The obtained abstract result is applied to study a class of initial-boundary value problems to time-fractional order equations with polynomials of an elliptic self-adjoint differential operator with respect to spatial variables as linear operators at the time-fractional derivatives. The nonlinear operator in the considered partial differential equations is assumed to be smooth with respect to phase variables.

【 授权许可】

Unknown