A generalized fractional (q, h)–Gronwall inequality and its applications to nonlinear fractional delay (q, h)–difference systems

Du, Feifei; Jia, Baoguo

doi:10.1002/mma.7426

Cited by 8 publications

References 29 publications

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Exploring a new discrete delayed Mittag–Leffler matrix function to investigate finite‐time stability of Riemann–Liouville fractional‐order delay difference systems

2022

Math Methods in App Sciences

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In this paper, firstly, a new discrete delayed Mittag–Leffler matrix function is introduced, which generalizes the existing discrete delayed exponential matrix function. Secondly, based on it, the explicit formula of the solution of homogeneous Riemann–Liouville (RL) fractional‐order delay difference system is obtained. Thirdly, the explicit formulas of the solutions of nonhomogeneous RL fractional‐order delay difference systems are also derived in terms of the superposition principle and the new discrete delayed Mittag–Leffler matrix function. Furthermore, a finite‐time stability (FTS) criterion of nonhomogeneous RL fractional‐order delay difference system is given using the properties of the new discrete delayed Mittag–Leffler matrix function. Finally, three examples are presented to demonstrate the effectiveness of the proposed theorems.

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Exploring a new discrete delayed Mittag–Leffler matrix function to investigate finite‐time stability of Riemann–Liouville fractional‐order delay difference systems

2022

Math Methods in App Sciences

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On implicit fractional q‐difference equations: Analysis and stability

Laledj

Salim

Lazreg

et al. 2022

Math Methods in App Sciences

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This paper deals with some existence and Ulam stability results for some classes of implicit fractional q-difference equations with and without random effects in Banach spaces and Banach algebras. Our results are provided by applying the fixed point theory (Itoh's random fixed point theorem, the nonlinear alternative of Schaefer's type proved by Dhage, and an other Dhage's random fixed point theorem in Banach algebras). Other results about the extremal solutions and random extremal solutions under Carathéodory and certain monotonicity conditions are proved. In the final section, some illustrative examples are provided.

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Fractional quantum Julia set

Wang

2023

Applied Mathematics and Computation

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A generalized fractional (q, h)–Gronwall inequality and its applications to nonlinear fractional delay (q, h)–difference systems

Cited by 8 publications

References 29 publications

Exploring a new discrete delayed Mittag–Leffler matrix function to investigate finite‐time stability of Riemann–Liouville fractional‐order delay difference systems

Exploring a new discrete delayed Mittag–Leffler matrix function to investigate finite‐time stability of Riemann–Liouville fractional‐order delay difference systems

On implicit fractional q‐difference equations: Analysis and stability

Fractional quantum Julia set

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