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Journal articles on the topic 'Integral Solutions'

Author: Grafiati

Published: 3 June 2025

Last updated: 31 July 2025

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1

Bellour, Azzeddine, Mahmoud Bousselsal, and Mohamed-Aziz Taoudi. "Integrable solutions of a nonlinear integral equation related to some epidemic models." Glasnik Matematicki 49, no. 2 (2014): 395–406. http://dx.doi.org/10.3336/gm.49.2.12.

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2

Hartmann, Friedel. "Fe-solutions are integral solutions." Communications in Applied Numerical Methods 3, no. 6 (1987): 483–84. http://dx.doi.org/10.1002/cnm.1630030607.

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3

Dhage, Bapurao, Janhavi Dhage, and Shyam Dhage. "On existence of extremal integrable solutions and integral inequalities for nonlinear Volterra type integral equations." Malaya Journal of Matematik 12, no. 03 (2024): 245–52. http://dx.doi.org/10.26637/mjm1203/002.

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We prove the existence of maximal and minimal integrable solutions of nonlinear Volterra type integral equations. Two basic integral inequalities are obtained in the form of extremal integrable solutions which are further exploited for proving the boundedness and uniqueness of the integrable solutions of the considered integral equation.

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4

B. Dhage, Janhavi, Shyam B. Dhage, and Bapurao C. Dhage. "ON EXISTENCE OF EXTREMAL INTEGRABLE SOLUTIONS AND INTEGRAL INEQUALITIES FOR NONLINEAR URYSOHN TYPE INTEGRAL EQUATIONS." jnanabha 54, no. 02 (2024): 300–305. https://doi.org/10.58250/jnanabha.2024.54230.

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We prove the existence of maximal and minimal integrable solutions of nonlinear Urysohn type integral equations. Two basic integral inequalities are obtained in the form of extremal integrable solutions which are further exploited for proving the boundedness and uniqueness of the integrable solutions of the considered integral equation.

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5

Banaś, Józef. "Integrable solutions of Hammerstein and Urysohn integral equations." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 46, no. 1 (1989): 61–68. http://dx.doi.org/10.1017/s1446788700030378.

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AbstractIn this paper we prove theorems on the existence of integrable and monotonic solutions of Hammserstein and Urysohn integral equations. The basic tool used in the proof is the fixed point principle for contractions with respect to the so-called measure of weak noncompactness.

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6

CUBIOTTI, PAOLO. "Integrable solutions of highly discontinuous implicit functional-integral equations." Optimization Eruditorum 1, no. 2 (2024): 75–87. https://doi.org/10.69829/oper-024-0102-ta01.

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7

Balachandran, K., and S. Ilamaran. "A note on integrable solutions of Hammerstein integral equations." Proceedings of the Indian Academy of Sciences - Section A 105, no. 1 (1995): 99–103. http://dx.doi.org/10.1007/bf02840593.

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8

Cichoń, Mieczysław, and Mohamed M. A. Metwali. "On Monotonic Integrable Solutions for Quadratic Functional Integral Equations." Mediterranean Journal of Mathematics 10, no. 2 (2012): 909–26. http://dx.doi.org/10.1007/s00009-012-0218-0.

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9

Shadimetov, Kh M., and D. M. Akhmedov. "An optimal approximate solution of the I kind Fredholm singular integral equations." Filomat 38, no. 30 (2024): 10765–96. https://doi.org/10.2298/fil2430765s.

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In this work, we study the problem of profile and lattice profile in aerodynamics. The first kind of Fredholm singular integral equation solves this problem. The Cauchy-type singular integrals are solutions to the first kind of Fredholm singular integral equation. However, the antiderivative function of these singular integrals can only be found in some cases. To overcome this, we utilize the Sobolev method to create an optimal quadrature formula for Cauchy-type singular integrals. By doing so, we can approximately solve the Fredholm integral equation of type I with higher accuracy. We compare

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10

Kolodii, A. M. "Continuous solutions of volterra integral equations with curvilinear stochastic integrals." Journal of Soviet Mathematics 67, no. 4 (1993): 3187–96. http://dx.doi.org/10.1007/bf01261276.

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11

Ren, Zhengyong, Huang Chen, Jingtian Tang, and Feng Zhou. "A volume-surface integral approach for direct current resistivity problems with topography." GEOPHYSICS 83, no. 5 (2018): E293—E302. http://dx.doi.org/10.1190/geo2017-0577.1.

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We have developed an accurate volume-surface integral formula for 3D direct current (DC) resistivity forward modeling with heterogeneous conductivities and arbitrary homogeneous topography. First, a volume-surface integral formula is derived from its elliptic boundary value problem in terms of an artificial analytical function defined over the full space. That leads to a volume integral accounting for underground anomalous regions and a surface integral over the surface topography. Then, tetrahedral grids are used to discretize the volume anomalous bodies and triangular grids are adopted to ap

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12

Tzoulis, A., and T. F. Eibert. "Review of singular potential integrals for method of moments solutions of surface integral equations." Advances in Radio Science 2 (May 27, 2005): 93–99. http://dx.doi.org/10.5194/ars-2-93-2004.

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Abstract. Accurate evaluation of singular potential integrals is essential for successful method of moments (MoM) solutions of surface integral equations. In mixed potential formulations for metallic and dielectric scatterers, kernels with 1/R and r1/R singularities must be considered. Several techniques for the treatment of these singularities will be reviewed. The most common approach solves the MoM source integrals analytically for specific observation points, thus regularizing the integral. However, in the case of r1/R a logarithmic singularity remains for which numerical evaluation of the

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13

Meehan, Maria, and Donal O'regan. "Positive solutions of Volterra integral equations using integral inequalities." Journal of Inequalities and Applications 2002, no. 2 (2002): 465397. http://dx.doi.org/10.1155/s1025583402000140.

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14

Leksin, V. P. "Integral Solutions to Schlesinger Equations." Journal of Mathematical Sciences 208, no. 2 (2015): 229–39. http://dx.doi.org/10.1007/s10958-015-2440-3.

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15

Medved, Milan, Michal Pospíšil та Eva Brestovanská. "Nonlinear integral inequalities involving Ψ -Hilfer fractional integrals and iterated fractional integrals, with applications to Ψ -Caputo fractional differential equations". Electronic Journal of Qualitative Theory of Differential Equations, № 30 (2025): 1–24. https://doi.org/10.14232/ejqtde.2025.1.30.

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In this paper, modifications of the well-known desingularization method proposed by the first author are used to derive nonlinear versions of the Henry--Gronwall inequality for integral inequalities with the Ψ -Hilfer fractional integral, as well as nonlinear integral inequalities with iterated Ψ -Hilfer fractional integrals. The results are applied to obtain bounds for solutions of initial value problems for nonlinear Ψ -Caputo fractional differential equations, and sufficient conditions for the non-existence of blowing-up solutions.

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16

El-Sayed, Ahmed, and Hind H. G. Hashem. "Integrable and continuous solutions of a nonlinear quadratic integral equation." Electronic Journal of Qualitative Theory of Differential Equations, no. 25 (2008): 1–10. http://dx.doi.org/10.14232/ejqtde.2008.1.25.

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17

Abdel Hamid, Haydar, and Waad Al Sayed. "Integrable solutions of a generalized mixed-type functional integral equation." Applied Mathematics and Computation 276 (March 2016): 356–66. http://dx.doi.org/10.1016/j.amc.2015.12.024.

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18

Zhou, Mi, Hengtai Wang, Zhenghua Xu, and Lu Zhang. "The Study of Fractional Quadratic Integral Equations Involves General Fractional Integrals." Fractal and Fractional 9, no. 4 (2025): 249. https://doi.org/10.3390/fractalfract9040249.

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This paper investigates the well-posedness of analytical solutions to fractional quadratic differential equations, which involve generalized fractional integrals with respect to other functions. The nonlinear components f and h depend on spatial variables and the general fractional integral, respectively. We use the operator equation T1ωT2ω+T3ω=ω to investigate the existence of solutions, marking the first study of its kind. Using an auxiliary function and Boyd and Wang’s fixed-point theorem, the uniqueness and continuous dependence of the solution are obtained. In particular, we applied nonli

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19

Turmetov, B. Kh, and Z. N. Baimetova. "On an operator method for constructing solutions to integral and differential equations with a singularity." Q A Iasaýı atyndaǵy Halyqaralyq qazaq-túrіk ýnıversıtetіnіń habarlary (fızıka matematıka ınformatıka serııasy) 26, no. 3 (2023): 7–27. http://dx.doi.org/10.47526/2023-3/2524-0080.01.

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In this paper, we consider new classes of fractional integral and derivative. These operators are generalizations of well-known integrals and the Riemann-Liouville derivative and the Caputo derivative. The article considers an operator method for solving integral and differential equations of fractional order. This method is based on the construction of normalized systems with respect to integral and differential operators. The algorithm for constructing normalized systems is given in the form of four steps. This method is first used to construct solutions to linear integral equations with con

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20

Darwish, Mohamed Abdalla. "On monotonic solutions of an integral equation of Abel type." Mathematica Bohemica 133, no. 4 (2008): 407–20. http://dx.doi.org/10.21136/mb.2008.140629.

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21

LIU, WEI, GUOJU YE, YING WANG, and XUEYUAN ZHOU. "ON PERIODIC SOLUTIONS FOR FIRST-ORDER DIFFERENTIAL EQUATIONS INVOLVING THE DISTRIBUTIONAL HENSTOCK–KURZWEIL INTEGRAL." Bulletin of the Australian Mathematical Society 86, no. 2 (2012): 327–38. http://dx.doi.org/10.1017/s0004972711003455.

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AbstractThe purpose of this paper is to study the existence of periodic solutions and the topological structure of the solution set of first-order differential equations involving the distributional Henstock–Kurzweil integral. The distributional Henstock–Kurzweil integral is a general integral, which includes the Lebesgue and Henstock–Kurzweil integrals. The main results extend some previously known results in the literature.

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22

Muddassar, Muhammad, Tahira Jabeen, and Hira Perveen. "On Inequalities of Trapezium Type Via Fractional Integrals Operators." International Journal of Emerging Multidisciplinaries: Mathematics 1, no. 2 (2022): 58–70. http://dx.doi.org/10.54938/ijemdm.2022.01.2.42.

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In this article, we get solutions of some integral inequalities of Hermite-Hadamard type and using the approach of ($\psi$,$h$)-Convex function by the way of Riemann-Liouville Fractional integrals and Katugampola Fractional integral operators.

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23

Aldosary, Saud Fahad, Mohamed M. A. Metwali, Manochehr Kazemi, and Ateq Alsaadi. "On integrable and approximate solutions for Hadamard fractional quadratic integral equations." AIMS Mathematics 9, no. 3 (2024): 5746–62. http://dx.doi.org/10.3934/math.2024279.

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<abstract><p>This article addressed the integrable and approximate solutions of Hadamard-type fractional Gripenberg's equation in Lebesgue spaces $ L_1[1, e] $. It is well known that the Gripenberg's equation has significant applications in mathematical biology. By utilizing the fixed point (FPT) approach and the measure of noncompactness (MNC), we demonstrated the presence of monotonic integrable solutions as well as the uniqueness of the solution for the studied equation in spaces that are not Banach algebras. Moreover, the method of successive approximations was successfully app

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24

Dorogovtsev, A. A. "On Solutions of Integral Equations with an Extended Stochastic Integral." Theory of Probability & Its Applications 40, no. 3 (1996): 456–68. http://dx.doi.org/10.1137/1140050.

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25

Huang, Xiaoyu. "Solutions of Gaussian and Gauss-like integrals in Real and Complex Fields." Highlights in Science, Engineering and Technology 49 (May 21, 2023): 343–47. http://dx.doi.org/10.54097/hset.v49i.8531.

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The definite integrals play a vital role in many branches of natural science. Among them, the Gaussian integrals and Gaussian-like integrals are widely used in many fields, especially in statistics. Many times, the range of integration extends to the complex field. When people need to calculate these more complex integrals, they need some simpler methods to help them quickly calculate the integral value. This article describes how to solve Gaussian integrals and Gaussian-like integrals in real and complex domains. When calculating some complex integrals, integral transformations can be used, s

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26

Mikhailov, Mikhail D., and Renato M. Cotta. "CONVERGENCE ACCELERATION OF INTEGRAL TRANSFORM SOLUTIONS." Hybrid Methods in Engineering 3, no. 1 (2001): 6. http://dx.doi.org/10.1615/hybmetheng.v3.i1.70.

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27

Cichoń, Mieczysław, and Mohamed Metwali. "Monotonic solutions for quadratic integral equations." Discussiones Mathematicae. Differential Inclusions, Control and Optimization 31, no. 2 (2011): 157. http://dx.doi.org/10.7151/dmdico.1132.

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28

Frisch, H., C. V. M. Van Der Mee, and P. F. Zweifel. "Distributional solutions of singular integral equations." Journal of Integral Equations and Applications 2, no. 2 (1990): 205–10. http://dx.doi.org/10.1216/jie-1990-2-2-205.

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29

Meehan, Maria, and Donal O'Regan. "Positive Solutions of Singular Integral Equations." Journal of Integral Equations and Applications 12, no. 3 (2000): 271–80. http://dx.doi.org/10.1216/jiea/1020282208.

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30

Triebel, Hans. "Refined solutions of some integral equations." Functiones et Approximatio Commentarii Mathematici 29 (2001): 143–58. http://dx.doi.org/10.7169/facm/1538186724.

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31

CAHLON, B., and D. SCHMIDT. "Numerical solutions for functional integral equations." IMA Journal of Numerical Analysis 12, no. 4 (1992): 527–43. http://dx.doi.org/10.1093/imanum/12.4.527.

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32

Wong, Patricia J. Y. "Solutions for singular Volterra integral equations." Electronic Journal of Qualitative Theory of Differential Equations, no. 30 (2009): 1–15. http://dx.doi.org/10.14232/ejqtde.2009.4.30.

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33

Chiosi, Lou. "Integral Solutions of Unit Fraction Equations." School Science and Mathematics 86, no. 2 (1986): 137–43. http://dx.doi.org/10.1111/j.1949-8594.1986.tb11599.x.

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34

Cunningham, William H., and James F. Geelen. "Integral Solutions of Linear Complementarity Problems." Mathematics of Operations Research 23, no. 1 (1998): 61–68. http://dx.doi.org/10.1287/moor.23.1.61.

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35

Dominici, Diego. "Polynomial solutions of nonlinear integral equations." Journal of Physics A: Mathematical and Theoretical 42, no. 20 (2009): 205201. http://dx.doi.org/10.1088/1751-8113/42/20/205201.

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36

Georgiou, D. N., and I. E. Kougias. "Bounded solutions for fuzzy integral equations." International Journal of Mathematics and Mathematical Sciences 31, no. 2 (2002): 109–14. http://dx.doi.org/10.1155/s0161171202108258.

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37

Terbeche, Mekki, Constantin Sacaliuc, and Galina Vornicescu. "Solutions of some singular integral equation." Bulletin des Sciences Mathématiques 126, no. 5 (2002): 379–87. http://dx.doi.org/10.1016/s0007-4497(02)01116-8.

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38

Furumochi, Tetsuo. "Almost periodic solutions of integral equations." Nonlinear Analysis: Theory, Methods & Applications 30, no. 2 (1997): 845–52. http://dx.doi.org/10.1016/s0362-546x(96)00195-2.

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39

Ichiye, Toshiko, and A. D. J. Haymet. "Integral equation theory of ionic solutions." Journal of Chemical Physics 93, no. 12 (1990): 8954–62. http://dx.doi.org/10.1063/1.459234.

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40

Bugajewska, Daria, Dariusz Bugajewski та Henryk Hudzik. "BVφ-solutions of nonlinear integral equations". Journal of Mathematical Analysis and Applications 287, № 1 (2003): 265–78. http://dx.doi.org/10.1016/s0022-247x(03)00550-x.

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41

Tersian, Stepan A., and Petr P. Zabrejko. "Hammerstein Integral Equations with Nontrivial Solutions." Results in Mathematics 19, no. 1-2 (1991): 179–88. http://dx.doi.org/10.1007/bf03322425.

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42

Islam, M. N. "Periodic solutions of nonlinear integral equations." Annali di Matematica Pura ed Applicata 150, no. 1 (1988): 129–39. http://dx.doi.org/10.1007/bf01761466.

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43

van der Laan, Gerard, Dolf Talman, and Zaifu Yang. "Computing integral solutions of complementarity problems." Discrete Optimization 4, no. 3-4 (2007): 315–21. http://dx.doi.org/10.1016/j.disopt.2007.09.001.

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44

Huang, An, Bong H. Lian, Shing-Tung Yau, and Xinwen Zhu. "Chain integral solutions to tautological systems." Mathematical Research Letters 23, no. 6 (2016): 1721–36. http://dx.doi.org/10.4310/mrl.2016.v23.n6.a7.

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45

Islam, M. N. "Periodic solutions of Volterra integral equations." International Journal of Mathematics and Mathematical Sciences 11, no. 4 (1988): 781–92. http://dx.doi.org/10.1155/s016117128800095x.

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Consider the system of equationsx(t)=f(t)+∫−∞tk(t,s)x(s)ds, (1)andx(t)=f(t)+∫−∞tk(t,s)g(s,x(s))ds. (2)Existence of continuous periodic solutions of (1) is shown using the resolvent function of the kernelk. Some important properties of the resolvent function including its uniqueness are obtained in the process. In obtaining periodic solutions of (1) it is necessary that the resolvent ofkis integrable in some sense. For a scalar convolution kernelksome explicit conditions are derived to determine whether or not the resolvent ofkis integrable. Finally, the existence and uniqueness of continuous p

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46

Withers, Christopher S., and Saralees Nadarajah. "Series solutions to linear integral equations." Applied Mathematics and Computation 230 (March 2014): 218–30. http://dx.doi.org/10.1016/j.amc.2013.12.160.

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47

Alfawicka, Barbara. "Monotone solutions of Volterra integral equations." Journal of Mathematical Analysis and Applications 123, no. 1 (1987): 39–56. http://dx.doi.org/10.1016/0022-247x(87)90292-7.

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48

Mohan Reddy, J. "Integral equation solutions to surface irrigation." Journal of Agricultural Engineering Research 42, no. 4 (1989): 251–65. http://dx.doi.org/10.1016/0021-8634(89)90028-0.

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49

Hong, Shihuang, and Li Wang. "Existence of solutions for integral inclusions." Journal of Mathematical Analysis and Applications 317, no. 2 (2006): 429–41. http://dx.doi.org/10.1016/j.jmaa.2006.01.057.

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50

Benaroya, Haym. "Nonrecursive statistics for integral equation solutions." Applied Mathematics and Computation 24, no. 4 (1987): 275–80. http://dx.doi.org/10.1016/0096-3003(87)90011-7.

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