Related papers: Local existence and uniqueness for a fractional SI…
In this paper, we investigate existence and uniqueness of solutions for Darboux type problem for fuzzy fractional order differential equation. We used Caputo-Katogampola fuzzy fractional derivative for proving our results. Schauder's fixed…
The logistic growth model is a classical framework for describing constrained growth phenomena, widely applied in areas such as population dynamics, epidemiology, and resource management. This study presents a generalized extension using…
A numerical scheme for solving fractional initial value problems involving the Atangana-Baleanu fractional derivative is presented. Some examples for the proposed method are included, both for equations and systems of fractional initial…
In the present work, we discuss a unique solvability of an inverse-source problem with integral transmitting condition for time-fractional mixed type equation in a rectangular domain, where the unknown source term depends on space variable…
Following \cite{ipel1}, we consider a nonlinear SIS-type nonlocal system describing the spread of epidemics on networks, assuming nonlimited transmission, We prove local existence of a unique solution for any diffusion coefficients and…
In this paper, we investigate a fractional differential equation involving sequential Caputo derivatives, motivated by recent research on fractional models with multiple memory effects. Using techniques inspired by earlier works on…
In recent years, discrete fractional epidemic models with reaction-diffusion have become increasingly popular in the literature, not only for its necessity of numerical simulation, but also for its defined physical processes. In this paper,…
In this work, we investigate a unique solvability of a direct and inverse source problem for a time-fractional partial differential equation with the Caputo and Bessel operators. Using spectral expansion method, we give explicit forms of…
This work establishes the existence and uniqueness of solutions to the fractional diffusion equation $$\frac{\partial^\alpha u}{\partial t^{\alpha}} + K(-\Delta)^{\beta} u - \nabla \cdot (\nabla V u) = f$$ on a $d$-dimensional torus,…
We present some distinct asymptotic properties of solutions to Caputo fractional differential equations (FDEs). First, we show that the non-trivial solutions to a FDE can not converge to the fixed points faster than $t^{-\alpha}$, where…
We study a mathematical model of in situ leaching of rare metals, in which the joint filtration of two liquids is governed by the microscopic model $\mathbb{A}^{\varepsilon}$. A key difficulty is the unknown (free) boundary $\Gamma(r)$…
We consider the nonlinear Cauchy problem for $ \Psi $- Hilfer fractional differential equations and investigate the existence, interval of existence and uniqueness of solution in the weighted space of functions. The continuous dependence of…
The main objective of this article is to discuss the local existence of the solution to an initial value problem involving a non-linear differential equation in the sense of Riemann-Liouville fractional derivative of order $\sigma\in(1,2),$…
The first aim of this work is to establish a Peano type existence theorem for an initial value problem involving complex fractional derivative and the second is, as a consequence of this theorem, to give a partial answer to the local…
In this paper, we introduce a class of backward stochastic equations (BSEs) that extend classical BSDEs and include many interesting examples of generalized BSDEs as well as semimartingale backward equations. We show that a BSE can be…
This paper is devoted to the inverse problem of determining the spatially dependent source in a time fractional diffusion-wave equation, with the aid of extra measurement data at subboundary. Uniqueness result is obtained by using the…
In the present work, we have introduced and studied two epidemic models that are constructed with Caputo fractional derivative. We considered standard incidence rate and varying population dynamics for SIS and SIRS mathematical models.…
In this paper, we consider the following singularly perturbed fractional Kirchhoff problem \begin{equation*} \Big(\varepsilon^{2s}a+\varepsilon^{4s-N}…
In this paper, we investigate the existence and uniqueness of fixed point for partially ordered contraction type operators in Banach Space. We also present applications to integral and differential equations.
We discuss the existence, non-existence and multiplicity of nontrivial solutions for systems of Caputo fractional differential equations subject to nonlocal boundary conditions. Our methodology relies on classical fixed point index and we…