Olaniyi Samuel Iyiola

An inverse problem for a generalized fractional diffusion

We propose a method for determining the solution and source term of a generalized time-fractional diffusion equation. The method is based on selecting a bi-orthogonal basis of L 2 space corresponding to a nonself-adjoint boundary value problem. Uniqueness is proven and an existence result is obtained for smooth initial and final conditions. The asymptotic behavior of the generalized Mittag-Leffler function is used to relax the smoothness requirement on these conditions.

An iterative algorithm for solving split feasibility problems and fixed point problems in Banach spaces

The purpose of this paper is to study split feasibility problems and fixed point problems concerning left Bregman strongly relatively nonexpansive mappings in p-uniformly convex and uniformly smooth Banach spaces. We suggest an iterative scheme for the problem and prove strong convergence theorem of the sequences generated by our scheme under some appropriate conditions in real p-uniformly convex and uniformly smooth Banach spaces. Finally, we give numerical examples of our result to study its efficiency and implementation. Our result complements many recent and important results in this direction.

Convergence analysis of an iterative algorithm for fixed point problems and split feasibility problems in certain Banach spaces

In this paper, we introduce an iterative scheme for approximating a common element of the set of fixed points of left Bregman strongly nonexpansive mapping and the set of solutions of split feasibility problem. We further obtain a strong convergence result for finding a common solution of fixed point problem for left Bregman strongly nonexpansive mappings and split feasibility problem in the framework of -uniformly convex Banach spaces which are also uniformly smooth. We give an application of our result to approximating a solution of convexly constrained linear inverse problem which is also a fixed point of a left Bregman strongly nonexpansive mapping in -uniformly convex Banach spaces, which are also uniformly smooth. Finally, we give some numerical example of our result to study its efficiency and implementation. Our results complement many known related results in the literature.

Strong convergence result for monotone variational inequalities

Our aim in this paper is to study strong convergence results for L-Lipschitz continuous monotone variational inequality but L is unknown using a combination of subgradient extra-gradient method and viscosity approximation method with adoption of Armijo-like step size rule in infinite dimensional real Hilbert spaces. Our results are obtained under mild conditions on the iterative parameters. We apply our result to nonlinear Hammerstein integral equations and finally provide some numerical experiments to illustrate our proposed algorithm.

An inverse source problem for a two-parameter anomalous diffusion with local time datum

We determine the space-dependent source term for a two-parameter fractional diffusion problem subject to nonlocal non-self-adjoint boundary conditions and two local time-distinct datum. A bi-orthogonal pair of bases is used to construct a series representation of the solution and the source term. The two local time conditions spare us from measuring the fractional integral initial conditions commonly associated with fractional derivatives. On the other hand, they lead to delicate

Iterative methods for solving proximal split minimization problems

2\times 2

Strong convergence result for proximal split feasibility problem in Hilbert spaces

linear systems for the Fourier coefficients of the source term and of the fractional integral of the solution at

Strong convergence results for variational inequalities and fixed point problems using modified viscosity implicit rules

t=0

Iterative algorithms for solving variational inequalities and fixed point problems for asymptotically nonexpansive mappings in Banach spaces

. The asymptotic behavior and estimates of the generalized Mittag-Leffler function are used to establish the solvability of these linear systems, and to obtain sufficient conditions for the existence of our construction. Analytical and numerical examples are provided.

Solving k-Fractional Hilfer Differential Equations via Combined Fractional Integral Transform Methods

In this paper, we propose two iterative algorithms for finding the minimum-norm solution of a split minimization problem. We prove strong convergence of the sequences generated by the proposed algorithms. The iterative schemes are proposed in such a way that the selection of the step-sizes does not need any prior information about the operator norm. We further give some examples to numerically verify the efficiency and implementation of our new methods and compare the two algorithms presented. Our results act as supplements to several recent important results in this area.