On the existence of solutions for a multi-singular pointwise defined fractional system

One of best ways for increasing our abilities in exact modeling of natural phenomena is working with a singular version of different fractional differential equations. As is well known, multi-singular equations are a modern version of singular equations. In this paper, we investigate the existence of solutions for a multi-singular fractional differential system. We consider some particular boundary value conditions on the system. By using the α-ψ-contractions and locating some control conditions, we prove that the system via infinite singular points has solutions. Finally, we provide an example to illustrate our main result.

Stability analysis of a nonlinear coupled implicit switched singular fractional differential system with p-Laplacian

This paper deals with existence, uniqueness, and Hyers–Ulam stability of solutions to a nonlinear coupled implicit switched singular fractional differential system involving Laplace operator $\phi _{p}$ ϕ p . The proposed problem consists of two kinds of fractional derivatives, that is, Riemann–Liouville fractional derivative of order β and Caputo fractional derivative of order σ, where $m-1<\beta $ m − 1 < β , $\sigma < m$ σ < m , $m\in \{2,3,\dots \}$ m ∈ { 2 , 3 , … } . Prior to proceeding to the main results, the system is converted into an equivalent integral form by the help of Green’s function. Using Schauder’s fixed point theorem and Banach’s contraction principle, the existence and uniqueness of solutions are proved. The main results are demonstrated by an example.

Positive Solutions for(n-1,1)-Type Singular Fractional Differential System with Coupled Integral Boundary Conditions

We study the positive solutions of the(n-1,1)-type fractional differential system with coupled integral boundary conditions. The conditions for the existence of positive solutions to the system are established. In addition, we derive explicit formulae for the estimation of the positive solutions and obtain the unique positive solution when certain additional conditions hold. An example is then given to demonstrate the validity of our main results.

Existence Results for a Coupled System of Nonlinear Singular Fractional Differential Equations with Impulse Effects

A boundary value problem for the singular fractional differential system with impulse effects is presented. By applying Schauder's fixed point theorem in a suitably Banach space, we obtain the existence of at least one solution for this problem. Two examples are presented to illustrate the main theorem.