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Dergiler / Turkish Journal of Mathematics / 2020 / Cilt: 44 - Sayı: 3

Existence and uniqueness of solutions for nonlinear Caputo fractional difference equations

Churong CHEN
Martın BOHNER
Baoguo JIA
Sayfa
857–869
Yayın Tarihi
2020-05-01
DOI
—
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

We present two examples to illustrate our main results.

📌 3 Maddede Bu Makale

🎯
Amaç & Hipotez:We study two cases of nabla fractional Caputo difference equations.
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Temel Bulgular & Veri:Our main tool used is a Banach fixed pointtheorem, which allows us to give some existence and uniqueness theorems of solutions for discrete fractional Caputo equations.
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Sonuç & Katkı:We present two examples to illustrate our main results.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Nabla difference equation · existence and uniqueness · Caputo operator

Abstract

We study two cases of nabla fractional Caputo difference equations. Our main tool used is a Banach fixed pointtheorem, which allows us to give some existence and uniqueness theorems of solutions for discrete fractional Caputo equations. In addition, we develop the existence results for delta fractional Caputo difference equations, which correct ones obtained in Chen and Zhou. We present two examples to illustrate our main results.

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Bu Makaleye Atıf Yap

CHEN, C., BOHNER, M., JIA, B. (2020). Existence and uniqueness of solutions for nonlinear Caputo fractional difference equations. Turkish Journal of Mathematics, Cilt: 44 - Sayı: 3, 857–869. https://ajindex.com/articles/193201

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Kaynakça (11)

  1. Abdeljawad T. On Riemann and Caputo fractional differences. Computers and Mathematics with Applications 2011; 62 (3): 1602-1611
  2. Atici FM, Eloe PW. Two-point boundary value problems for finite fractional difference equations. Journal of Difference Equations and Applications 2011; 17 (4): 445-456
  3. Chen FL, Zhou Y. Existence and Ulam stability of solutions for discrete fractional boundary value problem. Discrete Dynamics in Nature Society 2013; Article ID 459161: 7 pages
  4. Du FF, Erbe L, Jia BG, Peterson AC. Two asymptotic results of solutions for nabla fractional (q, h)-difference equations. Turkish Journal of Mathematics 2018; 42 (5): 2214-2242
  5. Goodrich CS, Peterson AC. Discrete fractional calculus. Switzerland: Springer International Publishing, 2015
  6. Goodrich CS. Solutions to a discrete right-focal fractional boundary value problem. International Journal of Difference Equations 2010; 5 (2): 195-216
  7. Holm MT. The theory of discrete fractional calculus: development and application. PhD, University of Nebraska - Lincoln, Lincoln, NE, USA, 2011
  8. Reunsumrit J, Sitthiwirattham T. A new class of four-point fractional sum boundary value problems for nonlinear sequential fractional difference equations involving shift operators. Kragujevac Journal of Mathematics 2018; 42 (3): 371-387
  9. Sitthiwirattham T, Tariboon J, Ntouyas SK. Boundary value problems for fractional difference equations with three-point fractional sum boundary conditions. Advances in Difference Equations 2013; 296 (2013)
  10. Xie ZS, Jin YF, Hou CM. Multiple solutions for a fractional difference boundary value problem via variational approach. Abstract and Applied Analysis 2012; Article ID 143914: 16 pages
  11. Zeidler E. Nonlinear functional analysis and its applications I: Fixed-point theorems. Translated from the German by Peter R. Wadsack. New York, NY, USA: Springer-Verlag New York, 1986.