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We introduce an efficient variational hybrid quantum-classical algorithm designed for solving Caputo time-fractional partial differential equations. Our method employs an iterable cost function incorporating a linear combination of overlap…

In this paper, we investigate the existence and uniqueness of solutions for a fractional boundary value problem supplemented with nonlocal Riemann-Liouville fractional integral and Caputo fractional derivative boundary conditions. Our…

Classical Analysis and ODEs · Mathematics 2018-05-17 Faouzi Haddouchi

This paper presents a numerical method to solve a time-fractional Burgers equation, achieving order of convergence $(2-\alpha)$ in time, here $\alpha$ represents the order of the time derivative. The fractional derivative is modeled by…

Numerical Analysis · Mathematics 2025-08-29 Deeksha Singh , Swati Yadav , Rajesh K. Pandey

In the paper we deal with linear fractional control problems with constant delays in the state. Single-order systems with fractional derivative in Caputo sense of orders between 0 and 1 are considered. The aim is to introduce a new…

Numerical Analysis · Mathematics 2024-12-20 Josef Rebenda , Zdeněk Šmarda

In this work, we consider boundary value problems involving Caputo and Riemann-Liouville fractional derivatives of order $\alpha\in(1,2)$ on the unit interval $(0,1)$. These fractional derivatives lead to non-symmetric boundary value…

Numerical Analysis · Mathematics 2013-07-19 Bangti Jin , Raytcho Lazarov , Joseph Pasciak

In this paper, we propose a numerical scheme of the predictor-corrector type for solving nonlinear fractional initial value problems, the chosen fractional derivative is called the Atangana-Baleanu derivative defined in Caputo sense (ABC).…

Numerical Analysis · Mathematics 2022-05-10 Sami Aljhani , Mohd Salmi Md Noorani , Redouane Douaifia , Salem Abdelmalek

Much recent work has addressed the solution of a family of partial differential equations by computing the inverse operator map between the input and solution space. Toward this end, we incorporate function-valued reproducing kernel Hilbert…

Numerical Analysis · Mathematics 2022-04-05 Kaijun Bao , Xu Qian , Ziyuan Liu , Songhe Song

Existence and uniqueness of solutions for $\alpha\in\left( 2,3\right] $ order fractional differential equations with three point fractional boundary and integral conditions is discussed. The results are obtained by using standard fixed…

Dynamical Systems · Mathematics 2014-04-15 N. I. Mahmudov , S. Unul

In the present paper, we study a multipoint boundary value problem for a system of Fredholm integro-differenial equations by the method of parameterization. The case of a degenerate kernel is studied separately, for which we obtain…

Numerical Analysis · Mathematics 2023-09-28 Anar Assanova , Elmira Bakirova , Roza Uteshova

In this paper we consider a fully third order nonlinear boundary value problem which is of great interest of many researchers. First we establish the existence, uniqueness of solution. Next, we propose simple iterative methods on both…

Numerical Analysis · Mathematics 2020-04-24 Dang Quang A , Dang Quang Long

In this paper we present a method to solve initial value problems for fractional growth models, such as generalizations of the exponential and logistic with periodic harvesting models. Using a discretization of the Caputo derivative we…

Neural and Evolutionary Computing · Computer Science 2025-11-24 Juan Carlos Najera-Tinoco , Martin P. Arciga-Alejandre , Jorge Sanchez-Ortiz , Francisco J. Ariza-Hernandez

In this work we propose a novel approach to investigate boundary value problems (BVPs) for fully third order differential equations. It is based on the reduction of BVPs to operator equations for the nonlinear terms but not for the…

Numerical Analysis · Mathematics 2018-06-04 Dang Quang A , Dang Quang Long

We use reproducing kernel methods to study various rigidity problems. The methods and setting allow us to also consider the non-positive case.

Complex Variables · Mathematics 2007-09-18 Daniel Alpay , Simeon Reich , David Shoikhet

In this paper we develop a numerical scheme based on quadratures to approximate solutions of integro-differential equations involving convolution kernels, $\nu$, of diffusive type. In particular, we assume $\nu$ is symmetric and…

Numerical Analysis · Mathematics 2020-11-03 Loic Cappanera , Gabriela Jaramillo , Cory Ward

The aim of this study is to present a good modernistic strategy for solving some well-known classes of Lane-Emden type singular differential equations. The proposed approach is based on the reproducing kernel Hilbert space (RKHS) and…

Mean-field control problems have received continuous interest over the last decade. Despite being more intricate than in classical optimal control, the linear-quadratic setting can still be tackled through Riccati equations. Remarkably, we…

Optimization and Control · Mathematics 2023-08-23 Pierre-Cyril Aubin-Frankowski , Alain Bensoussan

In a rectangular domain, a boundary-value problem is considered for a mixed-type equation with a regularized Caputo-like counterpart of hyper-Bessel differential operator and the bi-ordinal Hilfer's fractional derivative. Using the method…

Analysis of PDEs · Mathematics 2022-06-28 E. Karimov , M. Ruzhansky , B. Toshtemirov

Many scientific problems involve data exhibiting both temporal and cross-sectional dependencies. While linear dependencies have been extensively studied, the theoretical analysis of regression estimators under nonlinear dependencies remains…

Statistics Theory · Mathematics 2025-02-27 Marie-Christine Düker , Adam Waterbury

We consider parametrized problems driven by spatially nonlocal integral operators with parameter-dependent kernels. In particular, kernels with varying nonlocal interaction radius $\delta > 0$ and fractional Laplace kernels, parametrized by…

Numerical Analysis · Mathematics 2019-10-02 Olena Burkovska , Max Gunzburger

Kernel-based approach to operator approximation for partial differential equations has been shown to be unconditionally stable for linear PDEs and numerically exhibit unconditional stability for non-linear PDEs. These methods have the same…

Numerical Analysis · Mathematics 2025-11-25 Andrew Christlieb , Sining Gong , Hyoseon Yang