ترغب بنشر مسار تعليمي؟ اضغط هنا

A Hilbert space approach to fractional differential equations

177   0   0.0 ( 0 )
 نشر من قبل Konrad Kitzing
 تاريخ النشر 2019
  مجال البحث
والبحث باللغة English




اسأل ChatGPT حول البحث

We study fractional differential equations of Riemann-Liouville and Caputo type in Hilbert spaces. Using exponentially weighted spaces of functions defined on $mathbb{R}$, we define fractional operators by means of a functional calculus using the Fourier transform. Main tools are extrapolation- and interpolation spaces. Main results are the existence and uniqueness of solutions and the causality of solution operators for non-linear fractional differential equations.



قيم البحث

اقرأ أيضاً

We formulate fractional difference equations of Riemann-Liouville and Caputo type in a functional analytical framework. Main results are existence of solutions on Hilbert space-valued weighted sequence spaces and a condition for stability of linear f ractional difference equations. Using a functional calculus, we relate the fractional sum to fractional powers of the operator $1 - tau^{-1}$ with the right shift $tau^{-1}$ on weighted sequence spaces. Causality of the solution operator plays a crucial role for the description of initial value problems.
We consider general difference equations $u_{n+1} = F(u)_n$ for $n in mathbb{Z}$ on exponentially weighted $ell_2$ spaces of two-sided Hilbert space valued sequences $u$ and discuss initial value problems. As an application of the Hilbert space appro ach, we characterize exponential stability of linear equations and prove a stable manifold theorem for causal nonlinear difference equations.
124 - X. G. Zhu , Y. F. Nie 2017
This article aims to develop a direct numerical approach to solve the space-fractional partial differential equations (PDEs) based on a new differential quadrature (DQ) technique. The fractional derivatives are approximated by the weighted linear com binations of the function values at discrete grid points on problem domain with the weights calculated via using three types of radial basis functions (RBFs) as test functions. The method in presence is robust, straight forward to apply, and highly accurate under the condition that the shape parameters of RBFs are well chosen. Numerical tests are provided to illustrate its validity and capability.
206 - Guo-cheng Wu 2010
Fractional variational approach has gained much attention in recent years. There are famous fractional derivatives such as Caputo derivative, Riesz derivative and Riemann-Liouville derivative. Sever
251 - Yingjun Jiang , Xuejun Xu 2015
We propose some multigrid methods for solving the algebraic systems resulting from finite element approximations of space fractional partial differential equations (SFPDEs). It is shown that our multigrid methods are optimal, which means the converge nce rates of the methods are independent of the mesh size and mesh level. Moreover, our theoretical analysis and convergence results do not require regularity assumptions of the model problems. Numerical results are given to support our theoretical findings.
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا