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Discrete delayed perturbation of Mittag-Leffler function and its application to linear fractional delayed difference system

Mustafa Aydin, Nazim I. Mahmudov

Abstract

The linear nonhomogeneous fractional difference system with constant coefficients is introduced. An explicit solution to the system is acquired by proposing a newly discrete retarded perturbation of the nabla Mittag-Leffer-type function containing such matrix equations that provide non-permutability. A couple of special cases obtained from our results are discussed.

Discrete delayed perturbation of Mittag-Leffler function and its application to linear fractional delayed difference system

Abstract

The linear nonhomogeneous fractional difference system with constant coefficients is introduced. An explicit solution to the system is acquired by proposing a newly discrete retarded perturbation of the nabla Mittag-Leffer-type function containing such matrix equations that provide non-permutability. A couple of special cases obtained from our results are discussed.
Paper Structure (8 sections, 12 theorems, 58 equations, 1 figure)

This paper contains 8 sections, 12 theorems, 58 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Discrete DPML function
  4. The explicit solution of RL fractional retarded difference system
  5. Homogeneous case:
  6. Nonhomogeneous case:
  7. Special Cases
  8. Conclusion

Key Result

Theorem 3

p1 Assume $z:\mathbb{N}_{a}\times\mathbb{N}_{a+1}\rightarrow\mathbb{R}$. Then

Figures (1)

  • Figure 1: Comparison of functions ${\mathbb{D}_{\alpha,\beta,r}^{M,N}}\left(k\right)$, $\mathbb{E}_{M,\alpha,\beta}(k,r)$, and $\mathbb{F}_r^{Nk^{\overline{\alpha}}}$ for $\alpha=0.9$, $\beta=0.6$, $M=5$, $N=3$, $r=2$.

Theorems & Definitions (27)

  • Definition 1
  • Definition 2
  • Theorem 3
  • Definition 4
  • Definition 5
  • Theorem 6
  • Lemma 7
  • Lemma 8
  • Definition 9
  • Remark 10
  • ...and 17 more