Multiple Positive Solutions for Nonlinear Fractional Differential Equations with Integral Boundary Value Conditions and a Parameter

Abstract

By using the theory of fixed-point index on cone for differentiable operators, spectral radii of some related linear integral operators, and properties of Green’s function, the existence of multiple positive solutions to a nonlinear fractional differential system with integral boundary value conditions and a parameter is established. At last, some examples are also provided to illustrate the validity of our main results.

Positive Solutions for a Class of Nonlinear Singular Fractional Differential Systems with Riemann–Stieltjes Coupled Integral Boundary Value Conditions

“…Many good results about fractional differential equations have been obtained in some recent literature. For more details, one can see [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17] and references therein. On the other side, the coupled problem of differential equations is one of the hot topics in applied mathematics, biology, biomathematics, and other fields.…”

Study on Implicit-Type Fractional Coupled System with Integral Boundary Conditions

“…Additionally, IBCs have useful applications in regularizing ill-posed parabolic backward problems in time partial differential equations-see, for example, mathematical models for bacterial self-regularization [29]. Some recent investigations on coupled systems of FDEs with IBCs can be found in [23,27,[30][31][32][33] and the references cited therein.…”

Controllability of Impulsive ψ-Caputo Fractional Evolution Equations with Nonlocal Conditions

“…Fractional systems have gained considerable popularity and importance due to their wide range of applications in many mathematical, physical, and engineering disciplines such as the chaotic synchronization system [1], solutions of differential systems [2][3][4], impulsive problems [5,6], quantum theory [7], diffusion phenomena [8][9][10], delay problems [11,12], systems of thermoelasticity [13,14], etc. It turns out that fractional calculus can provide a more vivid and accurate description of many practical problems than integral ones.…”