Existence and uniqueness results on time scales for fractional nonlocal thermistor problem in the conformable sense

Agarwal, Praveen; Ammi, Moulay Rchid Sidi; Asad, Jihad

doi:10.1186/s13662-021-03319-7

Cited by 15 publications

(16 citation statements)

References 23 publications

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“…Remark 3 If there is no impulse effect, then N = N = 0, and hence inequality (17) becomes 2Lξ < 1. Now, we present another result concerning the existence of S-asymptotically ω-periodic solutions for Problem (1).…”

Section: Then Y ∈ (X)mentioning

confidence: 99%

“…Based on Definition 2, we can give the definition of an S-asymptotically ω-periodic mild solution for Problem (1). J, E) is called an S-asymptotically ω-periodic mild solution for Problem (1) if it has the form…”

Section: Preliminaries and Notationsmentioning

confidence: 99%

“…Now, as a result of Steps 1-6, we conclude that is closed and completely continuous from D λ to the family on non-empty convex compact of D λ . Applying Lemma 3, has a fixed point which is an S-asymptotically ω-periodic mild solution to Problem (1).…”

Section: Then D Is Relatively Compact In Pc(j E)mentioning

confidence: 99%

“…Moreover, the technique presented in this paper can be used to generalize the work in [12,[15][16][17][18][19][20][21][23][24][25] to the case where the linear part is a sectorial operator, the nonlinear part is a multivalued function, and there is impulse effects. In addition, Problem (1) can be investigated on time scales using the arguments in [1], and using the arguments in [3,6,8], one can examine the asymptotic periodic solutions for Problem (1) when the Caputo derivative is replaced by the ψ-Caputo derivative, ψ-RL derivative, Atangana-Baleanu derivative or p-Laplacian operator. Also, the technique used in this paper can be applied to study the asymptotic periodic solutions for many fractional differential equations or inclusions generated by sectorial operators or almost sectorial operators.…”

mentioning

confidence: 99%

“…In Sect. 3, we provide two existence results of Sasymptotic ω-periodic solutions for Problem (1). In Sect.…”

mentioning

confidence: 99%

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Asymptotically periodic behavior of solutions to fractional non-instantaneous impulsive semilinear differential inclusions with sectorial operators

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In this paper, we prove two results concerning the existence of S-asymptotically ω-periodic solutions for non-instantaneous impulsive semilinear differential inclusions of order $1<\alpha <2$ 1 < α < 2 and generated by sectorial operators. In the first result, we apply a fixed point theorem for contraction multivalued functions. In the second result, we use a compactness criterion in the space of bounded piecewise continuous functions defined on the unbounded interval $J=[0,\infty )$ J = [ 0 , ∞ ) . We adopt the fractional derivative in the sense of the Caputo derivative. We provide three examples illustrating how the results can be applied.

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Section: Then Y ∈ (X)mentioning

confidence: 99%

Section: Preliminaries and Notationsmentioning

confidence: 99%

Section: Then D Is Relatively Compact In Pc(j E)mentioning

confidence: 99%

mentioning

confidence: 99%

“…In Sect. 3, we provide two existence results of Sasymptotic ω-periodic solutions for Problem (1). In Sect.…”

mentioning

confidence: 99%

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Asymptotically periodic behavior of solutions to fractional non-instantaneous impulsive semilinear differential inclusions with sectorial operators

2021

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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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Existence and Uniqueness Result of a Solution With Numeric Simulation for Nonlocal Thermistor Problem With the Presence of Memory Term

Dahi,

Sidi Ammi

2024

J Math Sci

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Existence and uniqueness results on time scales for fractional nonlocal thermistor problem in the conformable sense

Abstract: We study a conformable fractional nonlocal thermistor problem on time scales. Under an appropriate nonrestrictive condition on the resistivity function, we establish existence and uniqueness results. The proof is based on the use of Schauder’s point fixed theorem.

Cited by 15 publications

References 23 publications

Asymptotically periodic behavior of solutions to fractional non-instantaneous impulsive semilinear differential inclusions with sectorial operators

Asymptotically periodic behavior of solutions to fractional non-instantaneous impulsive semilinear differential inclusions with sectorial operators

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

Existence and Uniqueness Result of a Solution With Numeric Simulation for Nonlocal Thermistor Problem With the Presence of Memory Term

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