Related papers: Local existence and uniqueness for a fractional SI…
We show that any given function can be approximated with arbitrary precision by solutions of linear, time-fractional equations of any prescribed order. This extends a recent result by Claudia Bucur, which was obtained for time-fractional…
The center manifold is useful for describing the long-term behavior of a system of differential equations. In this work, we consider an autonomous differential equation in a Banach space that has the exponential trichotomy property in the…
In this paper, we used some theorems of fixed point for studying the results of existence and uniqueness for Hilfer-Hadamard-Type fractional differential equations, \[_{H}D^{\alpha,\beta}x(t)+f(t,x(t))=0, \hbox{ on the interval } J:=(1,e]\]…
We study a space-fractional Stefan problem with the Dirichlet boundary conditions. It is a model that describes superdiffusive phenomena. Our main result is the existence of the unique classical solution to this problem. In the proof we…
In this research, we provide a mathematical analysis for the novel coronavirus responsible for COVID-19, which continues to be a big source of threat for humanity. Our fractional-order analysis is carried out using a non-singular kernel…
We obtain the explicit expressions for the state probabilities of various state dependent fractional point processes recently introduced and studied by Garra et al. (2015). The inversion of the Laplace transforms of the state probabilities…
Research focus on optimal control problems brought on by fractional differential equations has been extensively applied in practice. However, because they are still open-ended and challenging, a number of problems with fractional…
The momentous objective of this work is to discuss some qualitative properties of solutions such as the estimate on the solutions, the continuous dependence of the solutions on initial conditions as well as the existence and uniqueness of…
In this article, we study the continuous and discrete fractional persistence problem which looks for the persistence of properties of a given classical ($\alpha=1$) differential equation in the fractional case (here using fractional…
We study the uniqueness, existence, and properties of bounded distributional solutions of the initial value problem problem for the anomalous diffusion equation $\partial_tu-\mathcal{L}^\mu [\varphi (u)]=0$. Here $\mathcal{L}^\mu$ can be…
It is studied the Cauchy problem for the equations of Burgers' type but with bounded dissipation flux. Such equations degenerate to hyperbolic ones as the velocity gradient tends to infinity. Thus the discontinuous solutions are permitted.…
Problem for the first order differential equation with an unbounded operator coefficient in Banach space and nonlinear nonlocal condition is considered. A numerical method is proposed and justified for the solution of this problem under…
This paper studies Langevin equation with nonlocal boundary conditions involving a $\psi$--Caputo fractional derivatives operator. By the aide of fixed point techniques of Krasnoselskii and Banach, we derive new results on existence and…
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…
We study a nonlocal thermistor problem for fractional derivatives in the conformable sense. Classical Schauder's fixed point theorem is used to derive the existence of a tube solution.
We study singular solutions to the fractional Laplace equation and, more generally, to nonlocal linear equations with measurable kernels. We establish B\^ocher type results that characterize the behavior of singular solutions near the…
This paper investigates quenching solutions of an one-dimensional, two-sided Riemann-Liouville fractional order convection-diffusion problem. Fractional order spatial derivatives are discretized using weighted averaging approximations in…
In this paper we study the class of mixed-index time fractional differential equations in which different components of the problem have different time fractional derivatives on the left hand side. We prove a theorem on the solution of the…
By means of two fractional order integral inequalities we investigate the existence and uniqueness of the solutions of the fractional nonlinear Volterra integral equation and a fractional nonlinear integrodifferential equation in Banach…
Epidemiological modeling is vital in understanding disease dynamics and guiding public health interventions. This study presents a time-fractional SEIR model to describe the transmission dynamics of Mpox, incorporating memory effects via…