On the existence and Ulam-Hyers stability of a new class of partial (Φ,χ)-fractional differential equations with impulses

Seemab, Arjumand; Rehman, ur Mujeeb; Fečkan, Michal; Alzabut, Jehad; Abbas, Syed

doi:10.2298/fil2106977s

Cited by 9 publications

(6 citation statements)

References 17 publications

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“…> 0 and for each solution (w 1 , z 1 ) ∈ W × Z of the inequality (15) there exists a solution (w, z) ∈ W × Z of the system (1) with…”

Section: Stability In Ulam-hyers-rassias Sensementioning

confidence: 99%

“…Recently, many researchers have exposed attention in the field of fractional differential equations theory, which will be used to describe phenomena of real-world problems. For more details; we refer the reader to the papers [5][6][7][8][9][10][11][12][13][14][15][16][17][18]. On the other hand, hybrid differential equations have gained extensive attention from many scholars; see for example [19][20][21].…”

Section: Introductionmentioning

confidence: 99%

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Existence and stability analysis to the sequential coupled hybrid system of fractional differential equations with two different fractional derivatives

Houas

Alzabut

Khuddush³

2023

Int. J. Optim. Control, Theor. Appl. (IJOCTA)

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In this paper, we discussed the existence, uniqueness and Ulam-type stability of solutions for sequential coupled hybrid fractional differential equations with two derivatives. The uniqueness of solutions is established by means of Banach's contraction mapping principle, while the existence of solutions is derived from Leray-Schauder's alternative fixed point theorem. Further, the Ulam-type stability of the addressed problem is studied. Finally, an example is provided to check the validity of our obtained results.

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“…> 0 and for each solution (w 1 , z 1 ) ∈ W × Z of the inequality (15) there exists a solution (w, z) ∈ W × Z of the system (1) with…”

Section: Stability In Ulam-hyers-rassias Sensementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Existence and stability analysis to the sequential coupled hybrid system of fractional differential equations with two different fractional derivatives

Houas

Alzabut

Khuddush³

2023

Int. J. Optim. Control, Theor. Appl. (IJOCTA)

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“…Fractional calculus has attracted considerable attention within the scientific community because of its diverse applications across various scientific disciplines. Among research areas of fractional calculus, a central point of interest for many authors has been on investigating the existence of solutions for the fractional differential equation (FDE) [1–7]. Lately, there has been a dedicated effort to examine the existence of solutions of especially the implicit FDE [8–13].…”

Section: Introductionmentioning

confidence: 99%

Implicit fractional differential equations: Existence of a solution revisited

Çelik,

Develi

2023

Math Methods in App Sciences

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This paper focuses on revisiting and improving the results regarding the existence of a solution to the implicit fractional differential equations (FDEs) given in the following form: for all with the initial condition , where is the Caputo fractional derivative (CFD). Mainly, we aim to weaken the necessary conditions often found in the literature for guaranteeing the existence of solution.

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“…Rassias provided a notable expansion of the Ulam-Hyers stability of maps by taking variables into account in 1978. [14][15][16].…”

Section: Introductionmentioning

confidence: 99%

Existence Solutions of ABC-Fractional Differential Equations with Periodic and Integral Boundary Conditions

Muhammad

Rafeeq

2022

J. Sci. Res.

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The nonlinear fractional differential equation (FDE) is discussed in this study. First, we will investigate the existence and uniqueness solution of the nonlinear differential equation to the Atangana-Baleanu fractional derivative in the sense of Caputo with the initial periodic condition and integral boundary condition by Krasnoselskii’s and Banach fixed point theorems. Then, we will study the Hyers-Ulam stability of our problem. Finally, we presented an example to demonstrate the use of our main theorems.

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On the existence and Ulam-Hyers stability of a new class of partial (Φ,χ)-fractional differential equations with impulses

Cited by 9 publications

References 17 publications

Existence and stability analysis to the sequential coupled hybrid system of fractional differential equations with two different fractional derivatives

Existence and stability analysis to the sequential coupled hybrid system of fractional differential equations with two different fractional derivatives

Implicit fractional differential equations: Existence of a solution revisited

Existence Solutions of ABC-Fractional Differential Equations with Periodic and Integral Boundary Conditions

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