Premium
Existence of solutions for a class of fractional difference equations at resonance
Author(s) -
Chen Huiqin,
Cui Yaqiong,
Kang Shugui,
Lu Youmin,
Feng Wenying
Publication year - 2021
Publication title -
studies in applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 46
eISSN - 1467-9590
pISSN - 0022-2526
DOI - 10.1111/sapm.12368
Subject(s) - mathematics , boundary value problem , mathematical analysis , operator (biology) , coincidence , nonlinear system , class (philosophy) , fractional calculus , differential equation , function (biology) , resonance (particle physics) , integral equation , physics , transcription factor , medicine , biochemistry , chemistry , alternative medicine , repressor , pathology , quantum mechanics , artificial intelligence , evolutionary biology , biology , computer science , gene , particle physics
Abstract We study a class of nonlinear fractional difference equations with nonlocal boundary conditions at resonance. The system is inspired by the three‐point boundary value problem for differential equations that have been extensively studied. It is also an extension to a fractional difference equation arising from real‐world applications. Converting the problem to an equivalent system corresponding to the integral operator and Green's function for differential equations, we are able to apply the coincidence degree theory for semilinear operators to obtain sufficient conditions for the existence of solutions. In addition, we prove a new property of the Gamma function and construct a family of examples to illustrate the applications of the results.