On Solvability of the Integro-Differential Equations

  • Faez Ghaffoori Mustansiriyah University, College of Basic Education
Keywords: Caratheodory conditions, Space of Lebesgue integrable, Schauder fixed point theorem, Integrodifferential Equation

Abstract

In this paper, we study the existence of solution to integro-differential equations in the space of Lebesgue-integrable  on un-bounded interval after transformed to nonlinear integral functional equation, the used tool is the fixed point theorem due to Schauder with weak measure of non compactness, due to De-Blasi. In addition, we give an example which satisfies the conditions of our existence theorem.

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References

[1] Faez N. Ghaffoori On existence and uniqueness of an integrable solution for a fractional Volterra integral equation on R^+. Iraq Journal of Science, 5(2020), 122-125
[2] P.P. Zarejko, A.I. Koshlev, M. A. Krasnoselskii,S. G. Mikhlin, L. S. Rakovshchik, V. J. Stecenko, Integral Equations, Noordhoff, Leyden, 1975.
[3] Mahmoud M. El-Borai, Wagdy G. El-Sayed, and Faez N. Ghaffoori, On the
Cauchy problem for some parabolic fractional partial differential equations with time delays J. of Math. And Sys. Sci. 6 (2016) 194-199.
[4] M. M. El-Borai, Khairia El-Said El-Nadi, Integrated semi groups and Cauchy
problems for some fractional abstract differential equations, Life Science Journal, 2013, 10(3), 793-795.
[5] J. Banas and K. Goebel, Measures of noncompactness in Banach spaces, Lectures notes in Pure and Appl. Math., 60 Dekker, New York-Basel (1980).
[6] J.Banas and Z. Knab, Integrable solutions of a functional integral equation Revista
Mathematica de la Univ. Complutense de Madrid, 2(1989), 31-38.
[7] J. Banas and Z. Knab, Measures of weak noncompactness and nonlinear integral equations of convolution type, J. Math. Anal. Appl., 146(1990), 353-362.
[8] J. Bana's and W. G. El-Sayed, Solvability of functional and Integral Equations in some classes of integrable functions, 1993.
[9] M. M. A. Metwali, Solvability of functional quadratic integral equations with perturbation, Opercula Math. 33, No. 4 (2013), 725-739.
[10] B. Recceri , A. Villani, Separability and Scorza Dragoni's property, Le-
Mathematic 37 (1982) 156-161.
[11] J. BANAS and J. RIVERO, On measures of weak noncompactness, Ann. Mat. Pura Appl. 151(1988), 213-224.
[12] J. BANAS and K. GOEBEL, Measures of noncompactness in Banach spaces, Lect. Notes in Math. 60, M. Dekker, New York and Basel 1980.
[13] F.S. De- BLASI, On a property of the unit sphere in Banach spaces, Bull. Math. Soc. Sci. Math. R. S. Roum. 21(1977), 259-262.
[14] N. DUNFORD and J. SCHWARTZ, Linear operators I, Int. Publ., Leyden 1963.

[15] J. BANAS and Z. KNAP, Measures of weak noncompactness and nonlinear integral equations of convolution type, J. Math. Anal Appl. 146(1990), 353-362.
[16] J. BANAS and W G. EL-SAYED, Measures of noncompactness and solvability of an integral equation in the class of functions of locally bounded variation, J. Math. Anal. Appl. 167(1992), 133-151.
[17] Ravi P. Agarwal, Maria Meehan and Donal O'regan, Fixed Point Theory and Applications Cambridge University Press, 2004.
Published
2022-01-06
How to Cite
Ghaffoori, F. (2022). On Solvability of the Integro-Differential Equations . Al-Qadisiyah Journal of Pure Science, 27(1), Math 1-9. https://doi.org/10.29350/qjps.2022.27.1.1466
Section
Mathematics