Abstract Fractional Cauchy Problem: Existence of Propagators and Inhomogeneous Solution Representation
نویسندگان
چکیده
We consider a Cauchy problem for the inhomogeneous differential equation given in terms of an unbounded linear operator A and Caputo fractional derivative order α∈(0,2) time. The previously known representation mild solution to such does not have conventional variation-of-constants like form, with propagator derived from associated homogeneous problem. Instead, it relies on existence two propagators different analytical properties. This fact limits theoretical especially numerical applicability existing representation. Here, we propose alternative that consolidates formulas sub-parabolic, parabolic sub-hyperbolic equations positive sectorial non-zero initial data. new is solely based and, therefore, can be considered as more natural extension classical By exploiting trade-off between regularity assumptions data powers right-hand side time, show proposed formula strongly convergent t≥0 under considerably weaker compared standard results literature. Crucially, achieved relaxation space ensures practically feasible any amenable evaluation using uniformly accurate quadrature-based algorithms.
منابع مشابه
Existence and blow-up of solution of Cauchy problem for the sixth order damped Boussinesq equation
In this paper, we consider the existence and uniqueness of the global solution for the sixth-order damped Boussinesq equation. Moreover, the finite-time blow-up of the solution for the equation is investigated by the concavity method.
متن کاملOn the Solvability of an Inverse Fractional Abstract Cauchy Problem
This note is devoted to study an inverse Cauchy problem in a Hilbert space H for fractional abstract differential equations of the form; ), ( ) ( ) ( = ) ( t g t f t u A dt t u d with the initial condition H u u = (0) 0 and the overdetermination condition: ), ( = ) ), ( ( t w v t u where (.,.) is the inner product in H , f is a real unknown function w is a given real function, 0 u , v ar...
متن کاملExistence and uniqueness of positive and nondecreasing solution for nonlocal fractional boundary value problem
In this article, we verify existence and uniqueness of positive and nondecreasing solution for nonlinear boundary value problem of fractional differential equation in the form $D_{0^{+}}^{alpha}x(t)+f(t,x(t))=0, 0
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Fractal and fractional
سال: 2023
ISSN: ['2504-3110']
DOI: https://doi.org/10.3390/fractalfract7100698