Abstract Nonlinear fractional differential equations have been intensely studied using fixed point theorems on various different function spaces. Here we combine theory with complex analysis, considering spaces of analytic functions and the behaviour powers. It is necessary to study carefully initial value properties Riemann–Liouville derivatives in order set up an appropriate problem, since so...

Abstract This paper describes the mathematical structure of ill-posed nonlinear inverse problem low-dose dental cone-beam computed tomography (CBCT) and explains advantages a deep learning-based approach to reconstruction images over conventional regularization methods. underlying reasons why CBCT is more than standard tomography. Despite this severe ill-posedness, demand for systems rapidly gr...

Ill-posedness of GNSS-based ionospheric tomography affects the stability and accuracy inversion results. Truncated singular value decomposition (TSVD) is a common algorithm reconstruction. However, TSVD method usually has low reconstruction efficiency. To resolve above problem, truncated mapping (TMSVD) presented to improve reconstructed computational authenticate effectiveness advantages TMSVD...

We consider numerical methods for a “quasi-boundary value” regularization of the backward parabolic problem given by { ut + Au = 0 , 0 < t < T u(T ) = f, where A is positive self-adjoint and unbounded. The regularization, due to Clark and Oppenheimer, perturbs the final value u(T ) by adding αu(0), where α is a small parameter. We show how this leads very naturally to a reformulation of the pro...

For an ill-posed problem which has its origin in several applications (e.g. electro-cardiology) a weak formulation is given over a Hilbert space without any constraints. This is achieved by means of Lagrangian multipliers. Beside theoretical questions (e.g. existence and uniqueness of a solutuion) a nite element approximation is considered. Error estimates, an investigation of the condition num...

THIS paper contains a preliminary examination o f the effect o f using the dichotomy (o, i ) instead o f actual measurement in the study o f relation­ ship. First, the simplest case possible is dealt w i t h , i n the hope o f inspiring, or provoking, more thorough treatment by others. O f course, dichotomy or other ordinal treatment has to be used when measure­ ment is inconceivable, e.g. when...