Existence and Uniqueness Results for Fractional (p, q)-Difference Equations with Separated Boundary Conditions

Neang, Pheak; Nonlaopon, Kamsing; Tariboon, Jessada; Ntouyas, Sotiris K.; Ahmad, Bashir

doi:10.3390/math10050767

Cited by 7 publications

(3 citation statements)

References 28 publications

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“…Then, By (27), we have L ≈ 0.0009667625 < 1. Hence, Theorem 7 concludes that the generalized sequential (p; q)-difference Navier problem (33) has at least one solution on I 0.25 (0.5;0.45) .…”

Section: Now By (26) We May Writementioning

confidence: 83%

“…so that D (p;q) and c D r (p;q) are the 1st order and r-th order (p; q)-difference and (p; q)derivative of the Caputo-like type, respectively, and E ∈ C([0, T p r ] × R, R). Once again in 2022, the same authors [33] defined a new function E ∈ C([0, T] × R, R) to simplify the domain of it, and to study the existence theorems, modeled the r-th order (p; q)-difference problem of the Caputo-like type as…”

Section: Introductionmentioning

confidence: 99%

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On Solutions of Two Post-Quantum Fractional Generalized Sequential Navier Problems: An Application on the Elastic Beam

Etemad,

Ntouyas,

Stamova

et al. 2024

Fractal Fract

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Fractional calculus provides some fractional operators for us to model different real-world phenomena mathematically. One of these important study fields is the mathematical model of the elastic beam changes. More precisely, in this paper, based on the behavior patterns of an elastic beam, we consider the generalized sequential boundary value problems of the Navier difference equations by using the post-quantum fractional derivatives of the Caputo-like type. We discuss on the existence theory for solutions of the mentioned (p;q)-difference Navier problems in two single-valued and set-valued versions. We use the main properties of the (p;q)-operators in this regard. Application of the fixed points of the ρ-θ-contractions along with the endpoints of the multi-valued functions play a fundamental role to prove the existence results. Finally in two examples, we validate our models and theoretical results by giving numerical models of the generalized sequential (p;q)-difference Navier problems.

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Section: Now By (26) We May Writementioning

confidence: 83%

Section: Introductionmentioning

confidence: 99%

On Solutions of Two Post-Quantum Fractional Generalized Sequential Navier Problems: An Application on the Elastic Beam

Etemad,

Ntouyas,

Stamova

et al. 2024

Fractal Fract

Self Cite

View full text Add to dashboard Cite

show abstract

“…Then, taking into account some fundamental fixed point theorems such as the Banach contraction principle, the Boyd-Wong fixed point theorem, and the Leray-Schauder nonlinear alternative, they provided the existence (uniqueness within some cases) of solutions to this problem under some certain conditions on f and constants. A variety of new results on (p, q)-difference equations via fixed point theory can be found in [18,19,[29][30][31]34]. Now, let us review basic definitions and theorems about (p, q)-calculus, which are found in [36].…”

Section: Introductionmentioning

confidence: 99%

Prešić-type fixed point results via Q-distance on quasimetric space and application to (p, q)-difference equations

Altun,

Gençtürk,

Erduran

2023

NAMC

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In this paper, we introduce two new properties to the Q-function, called as the 0-property and the small self-distance property, which is frequently used in studies of fixed point theory in quasimetric spaces. Then, with the help of Q-functions having these properties, we present some fixed point theorems for Prešić-type mappings in quasimetric spaces. Finally, we state a theorem for the existence and uniqueness of the solution to a boundary value problem for (p, q)-difference equations to demonstrate the applicability of our theoretical results, which we support with an example.

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Upper and lower solutions for an integral boundary problem with two different orders $\left ( p,q\right ) $-fractional difference

Mesmouli,

Al-Askar,

Mohammed

2024

J Inequal Appl

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In this paper, a $\left ( p,q\right ) $ ( p , q ) -fractional nonlinear difference equation of different orders is considered and discussed. With the help of $\left ( p,q\right ) $ ( p , q ) -calculus for integrals and derivatives properties, we convert the main integral boundary value problem (IBVP) to an equivalent solution in the form of an integral equation, we use the upper–lower solution technique to prove the existence of positive solutions. We present an example of the IBVP to apply and demonstrate the results of our method.

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Existence and Uniqueness Results for Fractional (p, q)-Difference Equations with Separated Boundary Conditions

Cited by 7 publications

References 28 publications

On Solutions of Two Post-Quantum Fractional Generalized Sequential Navier Problems: An Application on the Elastic Beam

On Solutions of Two Post-Quantum Fractional Generalized Sequential Navier Problems: An Application on the Elastic Beam

Prešić-type fixed point results via Q-distance on quasimetric space and application to (p, q)-difference equations

Upper and lower solutions for an integral boundary problem with two different orders $\left ( p,q\right ) $-fractional difference

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