Existence of Solutions for a Class of Caputo Fractional q-Difference Inclusion on Multifunctions by Computational Results

Samei, Mohammad Esmael; RANJBAR, GHORBAN KHALILZA DEH; Hedayati, Vahid

doi:10.46793/kgjmat2104.543s

Cited by 13 publications

(1 citation statement)

References 28 publications

(43 reference statements)

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“…With the attention of many experts and scholars on fractional q-difference, rich results have been achieved on fractional q-difference equations via q-Gronwall equality (see [18]), the existence and stability of the solutions for Riemann-Liouville fractional q-difference equations (see [19][20][21][22][23][24][25][26][27][28][29][30][31][32][33]), Caputo fractional q-difference initial boundary value problems (see [34][35][36][37][38][39]). In [40], Boutiara explored the mixed multi-term fractional q-difference equations with q-integral boundary conditions by using topological degree theory.…”

Section: Introductionmentioning

confidence: 99%

Nonlocal Problems for Hilfer Fractional q-Difference Equations

Tian

Yang

2023

Fractal Fract

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In the paper, we investigate a kind of Hilfer fractional q-difference equations with nonlocal condition. Firstly, the existence and uniqueness results of solutions are obtained by using topological degree theory and Banach fixed point theorem. Subsequently, the existence of extremal solutions in an ordered Banach space is discussed by monotone iterative method. In that following, we consider the Ulam stability results for equations. Finally, two examples are given to illustrate the effectiveness of theory results.

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Section: Introductionmentioning

confidence: 99%

Nonlocal Problems for Hilfer Fractional q-Difference Equations

Tian

Yang

2023

Fractal Fract

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Solutions of sum‐type singular fractional q integro‐differential equation with m‐point boundary value problem using quantum calculus

Ahmadian

Rezapour

Salahshour

et al. 2020

Math Methods in App Sciences

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Nowadays, many researchers have considerable attention to fractional calculus as a useful tool for modeling of different phenomena in the world. In this work, we investigate the sum‐type singular nonlinear fractional q integro‐differential equations with m‐point boundary value problem. The existence of positive solutions is obtained by the properties of the Green function, standard Caputo q derivative, Riemann–Liouville fractional q integral, and a fixed point theorem on a real Banach space scriptX, which has a partial order by using a cone P⊂scriptX. The proofs are based on solving the operators equation. By providing seven algorithms, four tables, and three figures, we give two numerical examples to illustrate our main result.

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On a fractional Caputo–Hadamard inclusion problem with sum boundary value conditions by using approximate endpoint property

Etemad

Rezapour

Samei

2020

Math Methods in App Sciences

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In the present research manuscript, we introduce a novel general fractional boundary value inclusion problem and investigate the necessary and sufficient conditions for desired existence results. Indeed, more precisely, we formulate a class of fractional multiterm Caputo-Hadamard differential inclusion problem with two-point sum boundary value conditions. In two separate theorems, we prove the existence results for mentioned inclusion problem by using-contractive maps and approximate endpoint property. Finally, we provide an example to illustrate our main results.

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Existence of Solutions for a Class of Caputo Fractional q-Difference Inclusion on Multifunctions by Computational Results

Cited by 13 publications

References 28 publications

Nonlocal Problems for Hilfer Fractional q-Difference Equations

Nonlocal Problems for Hilfer Fractional q-Difference Equations

Solutions of sum‐type singular fractional q integro‐differential equation with m‐point boundary value problem using quantum calculus

On a fractional Caputo–Hadamard inclusion problem with sum boundary value conditions by using approximate endpoint property

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