An existence result for Hadamard type two dimensional fractional functional integral equations via measure of noncompactness

Deep, Amar; Deepmala, _; Hazarika, Bipan

doi:10.1016/j.chaos.2021.110874

Cited by 20 publications

(3 citation statements)

References 15 publications

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“…[1][2][3][4]), and the recent research papers (cf. [5][6][7]). The theory of integral equations is speedily growing with the help of different studies of fixed point theory, topology, and functional analysis (cf.…”

Section: Introductionmentioning

confidence: 99%

An existence result with numerical solution of nonlinear fractional integral equations

Kazemi

Deep

Nieto

2023

Math Methods in App Sciences

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By utilizing the technique of Petryshyn's fixed point theorem in Banach algebra, we examine the existence of solutions for fractional integral equations, which include as special cases of many fractional integral equations that arise in various branches of mathematical analysis and their applications. Also, the numerical iterative method is employed successfully to find the solutions to fractional integral equations. Lastly, we recall some different cases and examples to verify the applicability of our study.

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Section: Introductionmentioning

confidence: 99%

An existence result with numerical solution of nonlinear fractional integral equations

Kazemi

Deep

Nieto

2023

Math Methods in App Sciences

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“…Darbo's fixed point theorem applies to study the existence, uniqueness, and stability of some equations such as neutral, stochastic, and Cauchy problems (see [9,5,10,20,21]) . Indeed, Darbo's fixed point theorem provides sufficient conditions that guarantee the existence of solutions for fixed point problems such as [8,19,12,23]. For example, the following integral equations x(ς) =f ς, x(α(ς)), β(ς) 0 g(ς, ℘, x(γ(℘))) d℘ , x(ς) =f ς, x(α(ς)), x(ς) =f (ς, x(ς))…”

Section: Introductionmentioning

confidence: 99%

Existence of solutions for some classes of integro-differential equations on C1(R+) by applying a measure of noncompactness

Tamimi

Saiedinezhad

Ghaemi

2022

Preprint

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This paper introduces sufficient conditions for the existence of solutions in some classes of integro-differential equations. Due to Darbo's fixed point theorem with an appropriate measure of noncompactness, we prove the existence of solution in each class of equations. Finally, some significant examples are solved using the artificial small parameter method.Mathematics Subject Classification (2010). 47H10, 45J05, 47H08.

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“…In [22], Kazemi et al used conditions (H1)-(H3) to check the fixed point existence solution of functional equation as z = T (z) = T 1 (z)T 2 (z), z ∈ C(I), where T 1 and T 2 are of the form (13). As in the previous two examples, the result of existence can be concluded.…”

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confidence: 99%

An existence result for implicit functional equations

Golshan

2023

Preprint

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In this article, we attempt to provide a more general method based on Petryshyn’s fixed-point theorem to ensure the existence of solutions to implicit functional equations. These implicit functional equations include fractional, non-fractional, (fractional) stochastic integral equations, etc., and any combination of them in C( I). Some results regarding the existence of fixed points in implicit functional integral equations will be reviewed in the literature. We show that this general result unifies and improves many of the main results in the literature. To illustrate that our approach is more general than other methods, we present some concrete examples. Also, we apply our method to create new functional equations in practice and check the existence of solutions.

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An existence result for Hadamard type two dimensional fractional functional integral equations via measure of noncompactness

Cited by 20 publications

References 15 publications

An existence result with numerical solution of nonlinear fractional integral equations

An existence result with numerical solution of nonlinear fractional integral equations

Existence of solutions for some classes of integro-differential equations on C1(R+) by applying a measure of noncompactness

An existence result for implicit functional equations

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