<doi_batch xmlns="http://www.crossref.org/schema/4.4.0" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" version="4.4.0"><head><doi_batch_id>855a1094-4140-4e49-8dd3-ba364a5f384d</doi_batch_id><timestamp>20241213082509816</timestamp><depositor><depositor_name>naun:naun</depositor_name><email_address>mdt@crossref.org</email_address></depositor><registrant>MDT Deposit</registrant></head><body><journal><journal_metadata language="en"><full_title>International Journal of Pure Mathematics</full_title><issn media_type="electronic">2313-0571</issn><archive_locations><archive name="Portico"/></archive_locations><doi_data><doi>10.46300/91019</doi><resource>http://www.naun.org/cms.action?id=6985</resource></doi_data></journal_metadata><journal_issue><publication_date media_type="online"><month>12</month><day>13</day><year>2024</year></publication_date><publication_date media_type="print"><month>12</month><day>13</day><year>2024</year></publication_date><journal_volume><volume>11</volume><doi_data><doi>10.46300/91019.2024.11</doi><resource>https://npublications.com/journals/puremath/2024.php</resource></doi_data></journal_volume></journal_issue><journal_article language="en"><titles><title>Noetherization Theory for a Singular Linear Differential Operator of Higher Order</title></titles><contributors><person_name sequence="first" contributor_role="author"><given_name>Abdourahman Haman</given_name><surname>Adji</surname><affiliation>Department of Mathematics and Computer Sciences, Faculty of Sciences, University of Ngaoundere, P.O.BOX 454, Ngaoundere, Cameroon</affiliation></person_name></contributors><jats:abstract xmlns:jats="http://www.ncbi.nlm.nih.gov/JATS1"><jats:p>Abdourahman Haman Adji</jats:p></jats:abstract><publication_date media_type="online"><month>12</month><day>13</day><year>2024</year></publication_date><publication_date media_type="print"><month>12</month><day>13</day><year>2024</year></publication_date><pages><first_page>1</first_page><last_page>10</last_page></pages><publisher_item><item_number item_number_type="article_number">1</item_number></publisher_item><ai:program xmlns:ai="http://www.crossref.org/AccessIndicators.xsd" name="AccessIndicators"><ai:free_to_read start_date="2024-12-13"/><ai:license_ref applies_to="am" start_date="2024-12-13">https://npublications.com/journals/puremath/2024/a022019-001(2024).pdf</ai:license_ref></ai:program><archive_locations><archive name="Portico"/></archive_locations><doi_data><doi>10.46300/91019.2024.11.1</doi><resource>https://npublications.com/journals/puremath/2024/a022019-001(2024).pdf</resource></doi_data><citation_list><citation key="ref0"><unstructured_citation>Ferziger J.H., Kaper H.G. Mathematical theory of Transport Processes in Gases (North-Holland Publ. Company, Amsterdam–London, 1972). </unstructured_citation></citation><citation key="ref1"><unstructured_citation>Hilbert D. Grundzüge einer allgemeinen Theorie der linear Integralgleichungen (Chelsea Publ. Company, New York, 1953). </unstructured_citation></citation><citation key="ref2"><doi>10.1007/bf03014061</doi><unstructured_citation>Picard E. “Un théorème général sur certaines équations intégrales de troisième espèce”, Comptes Rendus 150, 489–491 (1910). </unstructured_citation></citation><citation key="ref3"><doi>10.1016/0022-247x(81)90007-x</doi><unstructured_citation>Bart G.R. “Three theorems on third kind linear integral equations”, J. Math. Anal. Appl. 79, 48–57 (1981). DOI: https://doi.org/10.1016/0022-247X(81)90007-X. </unstructured_citation></citation><citation key="ref4"><doi>10.1137/0504053</doi><unstructured_citation>Bart G.R., Warnock R.L. “Linear integral equations of the third kind”, SIAM J. Math. Anal. 4, 609–622 (1973). DOI: https://doi.org/10.1137/0504053 </unstructured_citation></citation><citation key="ref5"><doi>10.1016/0022-247x(84)90096-9</doi><unstructured_citation>Sukavanam N. “A Fredholm-Type theory for third kind linear integral equations”, J. Math. Analysis Appl. 100, 478–484 (1984). DOI: https://doi.org/10.1016/0022- 247X(84)90096-9. </unstructured_citation></citation><citation key="ref6"><unstructured_citation>Shulaia D. “On one Fredholm integral equation of third kind”, Georgian Math. J. 4, 464–476 (1997). DOI: https://doi.org/10.1023/A:1022928500444. </unstructured_citation></citation><citation key="ref7"><doi>10.1515/gmj.2002.179</doi><unstructured_citation>Shulaia D. “Solution of a linear integral equation of third kind”, Georgian Math. J. 9, 179–196 (2002). DOI: https://doi.org/10.1515/GMJ.2002.179. </unstructured_citation></citation><citation key="ref8"><doi>10.1016/j.trmi.2017.05.002</doi><unstructured_citation>Shulaia D. “Integral equations of third kind for the case of piecewise monotone coefficients”, Transactions of A. Razmadze Math. Institute 171, 396–410 (2017). DOI: https://doi.org/10.1016/j.trmi.2017.05.002 </unstructured_citation></citation><citation key="ref9"><unstructured_citation>Rogozhin V.S., Raslambekov S.N. “Noether theory of integral equations of the third kind in the space of continuous and generalized functions”, Soviet Math. (Iz. VUZ) 23 (1), 48–53 (1979). </unstructured_citation></citation><citation key="ref10"><doi>10.1007/978-3-0348-8199-9_8</doi><unstructured_citation>Duduchava R.V .Singular integral equations on piecewise smooth curves in spaces of smooth functions (with L. P. Castro and F.-O. Speck). Toeplitz matrices and singular integral equations (Pobershau, 2001), 107– 144, Oper. Theory Adv. Appl., 135, Birkh¨auser, Basel, 2002. </unstructured_citation></citation><citation key="ref11"><unstructured_citation>Abdourahman A., Karapetiants N. “Noether theory for third kind linear integral equation with a singular linear differential operator in the main part”, Proceedings of A. Razmadze Math. Institute 135, 1–26 (2004). </unstructured_citation></citation><citation key="ref12"><doi>10.1088/0266-5611/16/4/308</doi><unstructured_citation>Bal G. Inverse problems for homogeneous transport equations: I. The one-dimensional case. Volume 16, Issue 4, pp. 997-1011 (2000).DOI: 10.1088/0266- 5611/16/4/308. </unstructured_citation></citation><citation key="ref13"><doi>10.1134/s0012266109090122</doi><unstructured_citation>Gabbassov N.S. “Methods for Solving an Integral Equation of the Third Kind with Fixed Singularities in the Kernel”, Diff. Equ. 45, 1341–1348 (2009). </unstructured_citation></citation><citation key="ref14"><doi>10.1007/s10625-006-0013-4</doi><unstructured_citation>Gabbassov N.S. “A Special Version of the Collocation Method for Integral Equations of the Third Kind”, Diff. Equ. 41, 1768–1774 (2005). </unstructured_citation></citation><citation key="ref15"><doi>10.1134/s0012266109090122</doi><unstructured_citation>N. S. Gabbasov, Methods for solving an integral equation of the third kind with fixed singularities in the kernel, Diff. Equ. 45 (2009), 1370-1378. DOI: https://doi.org/10.1134/S0012266109090122 </unstructured_citation></citation><citation key="ref16"><doi>10.1007/978-1-4612-0183-0</doi><unstructured_citation>Karapetiants N.S., Samko S.G. Equations with Involutive Operators (Birkhauser, Boston–Basel– Berlin, 2001). DOI: https://doi.org/10.1007/978-1- 4612-0183-0 </unstructured_citation></citation><citation key="ref17"><unstructured_citation>Prossdorf S. Some classes of singular equations (Mir, Moscow, 1979) [in Russian]. </unstructured_citation></citation><citation key="ref18"><doi>10.1063/1.1665929</doi><unstructured_citation>Bart G.R., Warnock R.L. “Solutions of a nonlinear integral equation for high energy scattering. III.Analyticity of solutions in a parameter explored numerically”, J. Math. Phys. 13, 1896–1902 (1972). </unstructured_citation></citation><citation key="ref19"><doi>10.1063/1.1666226</doi><unstructured_citation>Bart G.R., Johnson P.W., Warnock R.L., “Continuum ambiguity in the construction of unitary analytic amplitudes from fixed-energy scattering data”, J. Math. Phys. 14, 1558–1565 (1973). DOI: https://doi.org/10.1063/1.1666226 </unstructured_citation></citation><citation key="ref20"><doi>10.3103/s1066369x21110050</doi><unstructured_citation>E.Tompé Weimbapou1*, Abdourahman1**, and E. Kengne2***. «On Delta-Extension for a Noetherian Operator». ISSN 1066-369X, Russian Mathematics, 2021, Vol. 65, No. 11, pp. 34–45. c Allerton Press, Inc., 2021. DOI: https://doi.org/10.3103/S1066369X21110050. </unstructured_citation></citation><citation key="ref21"><unstructured_citation>Rogozhin V.S. Noether theory of operators. 2nd edition. Rostov-na- Donu:Izdat. Rostov Univ., 1982. 99 p. </unstructured_citation></citation><citation key="ref22"><doi>10.1007/s00020-013-2068-y</doi><unstructured_citation>Duduchava, R., Kverghelidze, N. &amp; Tsaava, M. Singular Integral Operators on an Open Arc in Spaces with Weight. Integr. Equ. Oper. Theory 77, 39–56 (2013). https://doi.org/10.1007/s00020-013-2068-y. </unstructured_citation></citation><citation key="ref23"><doi>10.1007/s10625-006-0013-4</doi><unstructured_citation>Gabbasov, N.S. A Special Version of the Collocation Method for Integral Equations of the Third Kind. Diff Equat 41, 1768–1774 (2005). https://doi.org/10.1007/s10625-006-0013-4. </unstructured_citation></citation><citation key="ref24"><doi>10.1007/978-3-642-61631-0</doi><unstructured_citation>Mikhlin, Solomon G., and Siegfried Prössdorf. Singular integral operators. Vol. 68. Springer Science &amp; Business Media, 1987. </unstructured_citation></citation><citation key="ref25"><unstructured_citation>Duduchava R.V. Singular integral equations in the Holder spaces with weight.I. Holder coefficients. Mathematics Researches. T.V, 2nd Edition. (1970) Pp 104-124. </unstructured_citation></citation><citation key="ref26"><unstructured_citation>Tsalyuk Z.B. Volterra Integral Equations//Itogi Nauki i Techniki. Mathematical analysis. V. 15. Moscow: VINITI AN SSSR. P. 131-199. </unstructured_citation></citation><citation key="ref27"><doi>10.1007/978-94-011-1180-5_3</doi><unstructured_citation>Kravchenko, V.G., Litvinchuk, G.S. (1994). The Noether theory of a singular integral functional operator of finite order in the continuous case. In: Introduction to the Theory of Singular Integral Operators with Shift. Mathematics and Its Applications, vol 289. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-1180- 5_3. </unstructured_citation></citation><citation key="ref28"><doi>10.1515/gmj.2002.179</doi><unstructured_citation>Shulaia.D. A Solution of a Linear Integral Equation of Third Kind. Georgian Mathematical Journal. Volume 9 (2002), Number 1, 179-196. DOI: https://doi.org/10.1515/GMJ.2002.179. </unstructured_citation></citation><citation key="ref29"><doi>10.1080/10652469708819143</doi><unstructured_citation>Yurko V. A. Integral transforms connected with differential operators having singularities inside the interval// Integral transforms and special functions.1997. V.5 N° 3-4 P.309-322. </unstructured_citation></citation><citation key="ref30"><unstructured_citation>Yurko V. A. On a differential operators of higher order with singularities inside the interval. Kratkie sochenie// Mathematicheskie Zamietkie, 2002. T.71, N° 1 P152- 156. </unstructured_citation></citation><citation key="ref31"><unstructured_citation>Abdourahman. Construction of Noether Theory for a Singular Linear Differential Operator. International Journal of Innovative Research in Sciences and Engineering Studies (IJIRSES). http:// www.ijirses.com ISSN: 2583-1658 | Volume: 2 Issue: 7 | 2022. Pp. 6-14.</unstructured_citation></citation></citation_list></journal_article></journal></body></doi_batch>