In this paper, we prove the existence of solutions for a boundary value problem involving both left Riemann-Liouville and right Caputo-type fractional derivatives. For this, we convert the posed problem to a sum of two integral operators, then we apply Krasnoselskii's fixed point theorem to conclude the existence of nontrivial solutions.

In this paper, by means of the Krasnoselskii fixed point theorem, the existence of solutions for a boundary value problem of nonlinear sequential fractional integro-differential equations are investigated. Two examples are given to illustrate our results.

Using Mawhin?s coincidence degree theory, we investigate the existence of solutions for a class of weighted p(t)-Laplacian boundary value problems at resonance and involving left and right Caputo fractional derivatives. An example is provided to illustrate the main existence results.

In this paper, we consider a mathematical model of a coronavirus disease involving the Caputo–Fabrizio fractional derivative by dividing the total population into the susceptible population $\mathcal{S}(t)$ S ( t ) , the vaccinated population $\mathcal{V}(t)$ V ( t ) , the infected population $\mathcal{I}(t)$ I ( t ) , the recovered population $\mathcal{R}(t)$ R ( t ) , and the death class $\mathcal{D}(t)$ D ( t ) . A core goal of this study is the analysis of the solution of a proposed mathematical model involving nonlinear systems of Caputo–Fabrizio fractional differential equations. With the help of Lipschitz hypotheses, we have built sufficient conditions and inequalities to analyze the solutions to the model. Eventually, we analyze the solution for the formed mathematical model by employing Krasnoselskii’s fixed point theorem, Schauder’s fixed point theorem, the Banach contraction principle, and Ulam–Hyers stability theorem.