On Sequential Fractional q-Hahn Integrodifference Equations

Dumrongpokaphan, Thongchai; Patanarapeelert, Nichaphat; Sitthiwirattham, Thanin

doi:10.3390/math8050753

Cited by 5 publications

(2 citation statements)

References 41 publications

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“…In the subsequent pace, Miller 23 introduced a composition of quantum differential equations and Lie theory and obtained some new results in this context. By following this trend in the next decades, numerous researchers generalized this theory and derived useful findings on the q-differential equations and inclusions (for more details, see previous studies [24][25][26][27][28][29][30][31][32] ).…”

Section: Introductionmentioning

confidence: 98%

On two structures of the fractional q‐sequential integro‐differential boundary value problems

Phương

Etemad

Rezapour

2021

Math Methods in App Sciences

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Our aim in the present research article is to discuss some existence aspects of solutions for two given fractional q-sequential structures of an integro-differential BVP in which the R.H.S. nonlinear term is regarded as two functions in both single-valued and multivalued versions. In addition to this, we formulate the boundary conditions in the framework of the mixed q-integro-derivative conditions simultaneously. For such new fractional q-sequential integro-differential structures, we utilize suitable standard analytical methods attributed to Krasnoselskii on the sum of two operators. In the final stage, we design two simulative examples to check the consistency of findings in the context of the proposed techniques.

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Section: Introductionmentioning

confidence: 98%

On two structures of the fractional q‐sequential integro‐differential boundary value problems

Phương

Etemad

Rezapour

2021

Math Methods in App Sciences

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“…Finally, Miller [28] combined quantum differential equations with Lie theory and investigated new theoretical results in this regard. By continuing this trend in the subsequent years, numerous researchers extended this field and obtained many interesting findings on the fractional quantum differential equations and inclusions (for more details, see [29][30][31][32][33][34][35][36][37][38][39][40][41][42][43][44][45][46][47][48]).…”

Section: Introductionmentioning

confidence: 99%

A novel fractional structure of a multi-order quantum multi-integro-differential problem

et al. 2020

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In the present research manuscript, we formulate a new generalized structure of the nonlinear Caputo fractional quantum multi-integro-differential equation in which such a multi-order structure of quantum integrals is considered for the first time. In fact, in the light of this type of boundary value problem equipped with the multi-integro-differential setting, one can simply study different cases of the existing usual integro-differential problems in the literature. In this direction, we utilize well-known analytical techniques to derive desired criteria which guarantee the existence of solutions for the proposed multi-order quantum multi-integro-differential problem. Further, some numerical examples are considered to examine our theoretical and analytical findings using the proposed methods.

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On two abstract Caputo multi-term sequential fractional boundary value problems under the integral conditions

Rezapour

Kumar

Iqbal

et al. 2022

Mathematics and Computers in Simulation

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On Sequential Fractional q-Hahn Integrodifference Equations

Abstract: In this paper, we prove existence and uniqueness results for a fractional sequential fractional q-Hahn integrodifference equation with nonlocal mixed fractional q and fractional Hahn integral boundary condition, which is a new idea that studies q and Hahn calculus simultaneously.

Cited by 5 publications

References 41 publications

On two structures of the fractional q‐sequential integro‐differential boundary value problems

On two structures of the fractional q‐sequential integro‐differential boundary value problems

A novel fractional structure of a multi-order quantum multi-integro-differential problem

On two abstract Caputo multi-term sequential fractional boundary value problems under the integral conditions

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