Existence of solutions for a class of nonlinear fractional difference equations of the Riemann–Liouville type

被引：0
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作者：
Pshtiwan Othman Mohammed
Hari Mohan Srivastava
Juan L. G. Guirao
Y. S. Hamed
机构：
[1] University of Sulaimani,Department of Mathematics, College of Education
[2] University of Victoria,Department of Mathematics and Statistics
[3] China Medical University,Department of Medical Research, China Medical University Hospital
[4] Azerbaijan University,Department of Mathematics and Informatics
[5] International Telematic University Uninettuno,Section of Mathematics
[6] Technical University of Cartagena,Department of Applied Mathematics and Statistics
[7] Taif University,Department of Mathematics and Statistics, College of Science
来源：
Advances in Continuous and Discrete Models | / 2022卷
关键词：
Discrete fractional calculus; Riemann–Liouville fractional calculus; Existence and uniquenes; Fixed-point theorems; Fractional difference equations; Falling fractional functions; 26A33; 39A12; 49K05;
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摘要：
Nonlinear fractional difference equations are studied deeply and extensively by many scientists by using fixed-point theorems on different types of function spaces. In this study, we combine fixed-point theory with a set of falling fractional functions in a Banach space to prove the existence and uniqueness of solutions of a class of fractional difference equations. The most important part of this article is devoted to correcting a significant mistake made in the literature in using the power rule by providing further conditions for its validity. Also, we provide specific conditions under which difference equations have attractive solutions and the solutions are also asymptotically stable. Furthermore, we construct some fractional difference examples in order to illustrate the validity of the observed results.
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