Multiplicity Solutions for Integral Boundary Value Problem of Fractional Differential Systems

Abstract

This paper deals with the existence and multiplicity of solutions for the integral boundary value problem of fractional differential systems: D0+α1u1t=f1t,u1t,u2t,D0+α2u2t=f2t,u1t,u2t,u10=0, D0+β1u10=0, D0+γ1u11=∫01D0+γ1u1ηdA1η,u20=0, D0+β2u20=0, D0+γ2u21=∫01D0+γ2u2ηdA2η,, where fi:0,1×0,∞×0,∞⟶0,∞ is continuous and αi−2<βi≤2,αi−γi≥1,2<αi≤3,γi≥1i=1,2.D0+α is the standard Riemann–Liouville’s fractional derivative of order α. Our result is based on an extension of the Krasnosel’skiĭ’s fixed-point theorem due to Radu Precup and Jorge Rodriguez-Lopez in 2019. The main results are explained by the help of an example in the end of the article.

Positive Solutions Depending on Parameters for a Nonlinear Fractional System withp-Laplacian Operators

“…During the past several decades, many fractional problems with differential equations have been paid much attention, see [1][2][3][4][5][6][7][8][9][10] for example. Also, much attention has been focused on the existence of positive solutions for such equations, see and the references therein.…”

Existence and Uniqueness of Positive Solutions for a New System of Fractional Differential Equations

“…In the case that the parameter μ satisfied some conditions, the existence of positive solutions for the boundary value problem (2) was proved. Meanwhile, many scholars considered some various fractional systems, such as [16][17][18][19][20][21][22][23][24][25][26][27][28][29][30] and the reference therein. For instance, in [16], the authors obtained the existence of two positive solutions for a nonlinear Caputo-type fractional system by virtue of fixed point index theory.…”