Measure of noncompactness on weighted Sobolev space with an application to some nonlinear convolution type integral equations

Najafabadi, Farzaneh Pouladi; Nieto, Juan J.; Kayvanloo, Hojjatollah Amiri

doi:10.1007/s11784-020-00809-1

Cited by 6 publications

(3 citation statements)

References 22 publications

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“…In this particular context, numerous writers have contributed scholarly papers on the topic of nonlinear integral equations, exploring the utilization of noncompactness measures and various other methodologies. Notably, the works of authors referenced as [4,10,12,13,14,15,21,17,18,19] delve into this subject matter. Aghajani et al, in their study [3], examined the possibility of solutions to the Cauchy problem for a fractional di¤erential equation.…”

Section: Introductionmentioning

confidence: 99%

Solvability of a System of Nonlinear Integral Equations with a General Kernel

Dehghan,

Roshan

2024

Preprint

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This study establishes the adequate conditions for the solvability of a Volterra-type nonlinear system of integral equations with some general kernels. The proof of the existence result is established in the space C (I; B 1 B 2), where B 1 and B 2 represent two arbitrary Banach spaces. Darbo’s fixed point theorem and the methodologies for noncompactness measures are employed in our analysis. Moreover, we study the Cauchy problem for a system of fractional di¤erential equations. Finally, we present some examples in sequence spaces that demonstrate the application of our results to specific kernels and a class of more general kernels that satisfy a specific condition. Mathematics Subject Classification: 47H08, 47G15, 47H10.

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Section: Introductionmentioning

confidence: 99%

Solvability of a System of Nonlinear Integral Equations with a General Kernel

Dehghan,

Roshan

2024

Preprint

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“…Recently, many researchers have studied approximate solutions of integral equations (cf. [26,31,[38][39][40]). Due to the error bound of the midpoint rule in connecting trapezoidal and Simpson rules and also according to the fact that trapezoidal and Simpson rules cannot be applied to approximate integrals that are not defined in the first and the endpoints of the integration, so we utilize the midpoint rule to find the approximate solutions of Equation (1).…”

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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“…More recently, authors in [15] constructed a new measure of noncompactness on weighted Sobolev spaces W m,p ω (Ω), where ω is A p weight, and presented the effectiveness of this measure by studying the existence of solution of some nonlinear convolutiontype integral equations using Darbo's fixed point theorem.…”

Section: Introductionmentioning

confidence: 99%

Solvability of a system of integral equations in two variables in the weighted Sobolev space $W^{1,1}_\omega(a,b)$ using a generalized measure of noncompactness

Shatnawi

Boudaoui

Shatanawi

et al. 2022

NAMC

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In this paper, we deal with the existence of solutions for a coupled system of integral equations in the Cartesian product of weighted Sobolev spaces E = Wω1,1 (a,b) x Wω1,1 (a,b). The results were achieved by equipping the space E with the vector-valued norms and using the measure of noncompactness constructed in [F.P. Najafabad, J.J. Nieto, H.A. Kayvanloo, Measure of noncompactness on weighted Sobolev space with an application to some nonlinear convolution type integral equations, J. Fixed Point Theory Appl., 22(3), 75, 2020] to applicate the generalized Darbo’s fixed point theorem [J.R. Graef, J. Henderson, and A. Ouahab, Topological Methods for Differential Equations and Inclusions, CRC Press, Boca Raton, FL, 2018].

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Measure of noncompactness on weighted Sobolev space with an application to some nonlinear convolution type integral equations

Cited by 6 publications

References 22 publications

Solvability of a System of Nonlinear Integral Equations with a General Kernel

Solvability of a System of Nonlinear Integral Equations with a General Kernel

An existence result with numerical solution of nonlinear fractional integral equations

Solvability of a system of integral equations in two variables in the weighted Sobolev space $W^{1,1}_\omega(a,b)$ using a generalized measure of noncompactness

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