Coinfection of Ebola virus and malaria is widespread, particularly in impoverished areas where malaria is already ubiquitous. Epidemics of Ebola virus disease arise on a sporadic basis in African nations with a high malaria burden. An observational study discovered that patients in Sierra Leone’s Ebola treatment centers were routinely infected with malaria parasites, increasing the risk of death. In this paper, we study Ebola-malaria coinfections under the generalized Mittag-Leffler kernel fractional derivative. The Banach fixed point theorem and the Krasnoselskii type are used to analyse the model’s existence and uniqueness. We discuss the model stability using the Hyers-Ulam functional analysis. The numerical scheme for the Ebola-malaria coinfections using Lagrange interpolation is presented. The numerical trajectories show that the prevalence of Ebola-malaria coinfections ranged from low to moderate depending on memory. This means that controlling the disease requires adequate knowledge of the past history of the dynamics of both malaria and Ebola. The graphical dynamics of the detection rate indicate that a variation in the detection rate only affects the following compartments: individuals that are latently infected with the Ebola, Ebola virus afflicted people who went unnoticed, individuals who have been infected with the Ebola virus and have been diagnosed with the disease, and persons undergoing Ebola virus therapy.

In this paper, we study the existence of multiple positive solutions for boundary value problems of high-order Riemann–Liouville fractional differential equations involving the p-Laplacian operator. Not only new existence conclusions of two positive solutions are obtained by employing functional-type cone expansion-compression fixed point theorem, but also some sufficient conditions for existence of at least three positive solutions are established by applying the Leggett–Williams fixed point theorem. In addition, we demonstrate the effectiveness of the main result by using an example.

In the article, the existence and uniqueness of positive solutions for a class of fractional differential equation with nonlinear boundary conditions are discussed. By applying some fixed point theorems on cone, we gain a unique positive solution and construct two iterative sequences to approximate the solution. Moreover, as applications of our main results, some examples are also presented.

In this paper, the blow up of solutions for a class of nonlinear parabolic equations u_t(x,t)=\nabla _{x}(a(u(x,t))b(x)c(t)\nabla _{x}u(x,t))+g(x,|\nabla _{x}u(x,t) |^2,t)f(u(x,t)) with mixed boundary conditions is studied. By constructing an auxiliary function and using Hopf's maximum principles, an existence theorem of blow-up solutions, upper bound of “blow-up time” and upper estimates of “blow-up rate” are given under suitable assumptions on a, b,c, f, g , initial data and suitable mixed boundary conditions. The obtained result is illustrated through an example in which a, b,c, f, g are power functions or exponential functions.

The primary objective of this research paper is to investigate two kinds of high-order tempered fractional differential equations integral boundary value problems. By means of the mixed monotone operators fixed point theorems with perturbation and the increasing $\varphi -(h,\sigma )$φ−(h,σ) -concave operators fixed point theorems, we can not only guarantee the existence-uniqueness of solution, but also construct successively sequences for approximating the unique solution. In addition, we demonstrate the effectiveness of the main result by using two examples.