Existence and Kummer Stability for a System of Nonlinear ϕ-Hilfer Fractional Differential Equations with Application

Mottaghi, Fatemeh; Li, Chenkuan; Abdeljawad, Thabet; Saadati, Reza; Ghaemi, Mohammad Bagher

doi:10.3390/fractalfract5040200

Cited by 5 publications

(1 citation statement)

References 13 publications

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“…Since the beginning in 1695 [1][2][3], fractional calculus (FC) has been building a great history and strengthening itself in various fields of science and engineering [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20]. Therefore, the FC field offers tremendous features for research.…”

Section: Introductionmentioning

confidence: 99%

Generalized derivatives and Laplace transform in (k,ψ)‐Hilfer form

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Mısır

Öğrekçi

2023

Math Methods in App Sciences

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In this work, we discuss the most generalized derivatives and integrals and their features in (k, 𝜓)-Hilfer form. Furthermore, we define the new generalized Laplace transform to the generalized derivatives and integrals in (k, 𝜓)-Hilfer form. Also, we have obtained the new generalized Laplace transforms of some expressions. These statements obtained cover many previous studies. Finally, we have given an example that will both use some of the results obtained and emphasize the importance of parameters such as k, 𝜌, 𝜓 of the (k, 𝜓)-generalized Laplace transform.

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Section: Introductionmentioning

confidence: 99%

Generalized derivatives and Laplace transform in (k,ψ)‐Hilfer form

Başcı

Mısır

Öğrekçi

2023

Math Methods in App Sciences

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Conditions to guarantee the existence of solutions for a nonlinear and implicit integro‐differential equation with variable coefficients

Saadati

Allahviranloo

2022

Math Methods in App Sciences

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Using Babenko's approach, multivariate Mittag–Leffler (MM–L) function, and Krasnoselskii's fixed point theorem, we first investigate the existence of solutions to a Liouville–Caputo nonlinear integro‐differential equation with variable coefficients and initial conditions in a Banach space. Then the existence of a positive solution for a variant equation is studied. Finally, we provide examples to illustrate the applications of the main results obtained.

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