Existence theory to a class of boundary value problems of hybrid fractional sequential integro-differential equations

We investigate the existence and uniqueness of solutions to a coupled system of the hybrid fractional integro-differential equations involving φ-Caputo fractional operators. To achieve this goal, we make use of a hybrid fixed point theorem for a sum of three operators due to Dhage and also the uniqueness result is obtained by making use of the Banach contraction principle. Moreover, we explore the Ulam–Hyers stability and its generalized version for the given coupled hybrid system. An example is presented to guarantee the validity of our existence results.

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“…. , m. In that work, Jamil et al proved the existence results with the help of Dhage's criterion [29].…”

Section: Introductionmentioning

confidence: 98%

“…Next in 2019, Jamil, Khan and Shah [29] studied the existence result for a boundary value problem of hybrid fractional sequential integro-differential equations involving Caputo derivatives given by…”

Section: Introductionmentioning

confidence: 99%

The generalized U–H and U–H stability and existence analysis of a coupled hybrid system of integro-differential IVPs involving φ-Caputo fractional operators

et al. 2021

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“…In [26] a discrete Gronwall inequality was introduced to provide a stability bound. In addition to these, some formulations as integro-differential equations have recently been analyzed by researchers [27][28][29][30][31][32][33].…”

Section: Introductionmentioning

confidence: 99%

Some Existence and Dependence Criteria of Solutions to a Fractional Integro-Differential Boundary Value Problem via the Generalized Gronwall Inequality

et al. 2021

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The main intention of the present research study is focused on the analysis of a Caputo fractional integro-differential boundary problem (CFBVP) in which the right-hand side of supposed differential equation is represented as a sum of two nonlinear terms. Under the integro-derivative boundary conditions, we extract an equivalent integral equation and then define new operators based on it. With the help of three distinct fixed-point theorems attributed to Krasnosel’skiĭ, Leray–Schauder, and Banach, we investigate desired uniqueness and existence results. Additionally, the dependence criterion of solutions for this CFBVP is checked via the generalized version of the Gronwall inequality. Next, three simulative examples are designed to examine our findings based on the procedures applied in the theorems.

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“…In 2015, similar results for fractional initial value problems involving hybrid integro-differential equations are established [40] by Sitho et al The existence problems of mild solution for hybrid fractional differential equations involving the Caputo fractional derivative of arbitrary order are investigated in [41] by Mahmudov in 2017. For similar research, refer to [42][43][44].…”

Section: Introductionmentioning

confidence: 99%

A study on multiterm hybrid multi-order fractional boundary value problem coupled with its stability analysis of Ulam–Hyers type

et al. 2021

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In this research work, a newly-proposed multiterm hybrid multi-order fractional boundary value problem is studied. The existence results for the supposed hybrid fractional differential equation that involves Riemann–Liouville fractional derivatives and integrals of multi-orders type are derived using Dhage’s technique, which deals with a composition of three operators. After that, its stability analysis of Ulam–Hyers type and the relevant generalizations are checked. Some illustrative numerical examples are provided at the end to illustrate and validate our obtained results.

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Existence theory to a class of boundary value problems of hybrid fractional sequential integro-differential equations

Cited by 19 publications

References 28 publications

The generalized U–H and U–H stability and existence analysis of a coupled hybrid system of integro-differential IVPs involving φ-Caputo fractional operators

The generalized U–H and U–H stability and existence analysis of a coupled hybrid system of integro-differential IVPs involving φ-Caputo fractional operators

Some Existence and Dependence Criteria of Solutions to a Fractional Integro-Differential Boundary Value Problem via the Generalized Gronwall Inequality

A study on multiterm hybrid multi-order fractional boundary value problem coupled with its stability analysis of Ulam–Hyers type

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