Existence results for a coupled system of nonlinear fractional multi-point boundary value problems at resonance

Abstract

By using the coincidence degree theory, we present an existence result for a coupled system of nonlinear fractional differential equations with multi-point boundary conditions at resonance.

On the solvability of a general class of a coupled system of stochastic functional integral equations

“…The uniqueness of the solution is investigated for Equations (1.1), and (1.2) as well. But due to some unexpected disturbance which may effect the accuracy of the system, we believe that stochastic models give more accurate results than the proposed models in (El-Sayed & Kenawy, 2014a, 2014b, see for more details (Elborai, Abdou, & Youssef, 2013a, 2013bElborai & Youssef, 2019;Klyatskin, 2015;Umamaheswari, Balachandran, & Annapoorani, 2017, 2018. Therefore, our aim in this article is to generalize the deterministic models 1.1, and 1.2 to the stochastic form in a suitable sense.…”

“…At the same time examining coupled systems associated with integral equations is important as well, because such systems model many physical problems, (see e.g. El-Sayed & Al-Fadel, 2018;Hashem & El-Sayed, 2017;Zhang, 2018). Recently ( 1.2) where 0 < b j < 1, j ¼ 1, 2, and J b j is the Riemann-Liouville fractional order integral operator.…”

Positive Solutions for a Hadamard Fractional p-Laplacian Three-Point Boundary Value Problem

“…where D α 0+ denotes the Riemann-Liouville fractional derivative. Positive solutions [16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35] and nontrivial solutions [36][37][38][39][40][41][42][43][44][45][46][47][48][49][50][51][52] were also studied for fractional-order equations. For example, the authors in [16] used the Guo-Krasnoselskii's fixed-point theorem and the Leggett-Williams fixed-point theorem to study the existence and multiplicity of positive solutions for the fractional boundary-value problem…”

Existence results of nonlocal boundary value problem for a nonlinear fractional differential coupled system involving fractional order impulses

“…As is well known, the study on fractional differential coupled systems is more complicated and challenged than the study on a single fractional differential equation. Recently, some scholars began to investigate fractional differential coupled systems and obtained some good results (see [8,12,13,24,26,31]). However, there are few papers on the impulsive fractional order coupled systems with nonlocal boundary conditions and impulses.…”