{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,5,14]],"date-time":"2025-05-14T04:48:15Z","timestamp":1747198095685,"version":"3.40.5"},"reference-count":20,"publisher":"Walter de Gruyter GmbH","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2023,2,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>In this paper, we prove the existence and uniqueness of Caputo time fractional pseudo-hyperbolic\nequations of higher order with purely nonlocal conditions of integral type.\nWe use an a priori estimate method; the so-called energy inequalities method,\nbased on some functional analysis tools, is developed for a Caputo time fractional of <jats:inline-formula id=\"j_anly-2021-0016_ineq_9999\">\n                     <jats:alternatives>\n                        <m:math xmlns:m=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                           <m:mrow>\n                              <m:mn>2<\/m:mn>\n                              <m:mo>\u2062<\/m:mo>\n                              <m:mi>m<\/m:mi>\n                           <\/m:mrow>\n                        <\/m:math>\n                        <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/j_anly-2021-0016_eq_0208.png\"\/>\n                        <jats:tex-math>{2m}<\/jats:tex-math>\n                     <\/jats:alternatives>\n                  <\/jats:inline-formula>-th and\n<jats:inline-formula id=\"j_anly-2021-0016_ineq_9998\">\n                     <jats:alternatives>\n                        <m:math xmlns:m=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                           <m:mrow>\n                              <m:mo stretchy=\"false\">(<\/m:mo>\n                              <m:mrow>\n                                 <m:mrow>\n                                    <m:mn>2<\/m:mn>\n                                    <m:mo>\u2062<\/m:mo>\n                                    <m:mi>m<\/m:mi>\n                                 <\/m:mrow>\n                                 <m:mo>+<\/m:mo>\n                                 <m:mn>1<\/m:mn>\n                              <\/m:mrow>\n                              <m:mo stretchy=\"false\">)<\/m:mo>\n                           <\/m:mrow>\n                        <\/m:math>\n                        <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/j_anly-2021-0016_eq_0169.png\"\/>\n                        <jats:tex-math>{(2m+1)}<\/jats:tex-math>\n                     <\/jats:alternatives>\n                  <\/jats:inline-formula>-th order and the density of the range of the operator generated by the considered problem.\nUsing the Laplace transform and homotopy perturbation, we find a semi-analytical solution.\nFinally, we give some examples for illustration.<\/jats:p>","DOI":"10.1515\/anly-2021-0016","type":"journal-article","created":{"date-parts":[[2022,10,25]],"date-time":"2022-10-25T15:51:01Z","timestamp":1666713061000},"page":"1-13","source":"Crossref","is-referenced-by-count":0,"title":["Existence and uniqueness of solutions to higher order fractional partial differential equations with purely integral conditions"],"prefix":"10.1515","volume":"43","author":[{"given":"Djamila","family":"Chergui","sequence":"first","affiliation":[{"name":"Department of Mathematics , Laboratory of Dynamical Systems and Control , University of Oum El Bouaghi , Oum El Bouaghi , Algeria"}]},{"given":"Ahcene","family":"Merad","sequence":"additional","affiliation":[{"name":"Department of Mathematics , Laboratory of Dynamical Systems and Control , University of Oum El Bouaghi , Oum El Bouaghi , Algeria"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0984-0159","authenticated-orcid":false,"given":"Sandra","family":"Pinelas","sequence":"additional","affiliation":[{"name":"CINAMIL \u2013 Centro de Investigac\u00e3o da Academia Militar , Academia Militar , Lisbo , Portugal"}]}],"member":"374","published-online":{"date-parts":[[2022,10,26]]},"reference":[{"key":"2023033112553352384_j_anly-2021-0016_ref_001","doi-asserted-by":"crossref","unstructured":"B.  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Anal. 9 (2004), 793\u2013813.","DOI":"10.1155\/S1085337504311061"},{"key":"2023033112553352384_j_anly-2021-0016_ref_008","doi-asserted-by":"crossref","unstructured":"A.  Bouziani,\nSolution of a transmission problem for semilinear parabolic-hyperbolic equations by the time-discretization method,\nJ. Appl. Math. Stoch. Anal. 2006 (2006), Article ID 61439.","DOI":"10.1155\/JAMSA\/2006\/61439"},{"key":"2023033112553352384_j_anly-2021-0016_ref_009","doi-asserted-by":"crossref","unstructured":"L.  Cveticanin,\nHomotopy-perturbation method for pure nonlinear differential equation,\nChaos Solitons Fractals 30 (2006), no. 5, 1221\u20131230.","DOI":"10.1016\/j.chaos.2005.08.180"},{"key":"2023033112553352384_j_anly-2021-0016_ref_010","unstructured":"L. C.  Evans,\nPartial Differential Equations,\nAmerican Mathematical Society, Providence, 1998."},{"key":"2023033112553352384_j_anly-2021-0016_ref_011","unstructured":"K. M.  Furati and N.  Tatar,\nAn existence result for a nonlocal fractional differential problem,\nJ. Fract. Calc. 26 (2004), 43\u201351."},{"key":"2023033112553352384_j_anly-2021-0016_ref_012","doi-asserted-by":"crossref","unstructured":"J.-H.  He,\nHomotopy perturbation technique,\nComput. Methods Appl. Mech. Engrg. 178 (1999), no. 3\u20134, 257\u2013262.","DOI":"10.1016\/S0045-7825(99)00018-3"},{"key":"2023033112553352384_j_anly-2021-0016_ref_013","unstructured":"A. A.  Kilbas, H. M.  Srivasta and J. J.  Trujillo,\nTheory and Applications of Fractional Differential Equations,\nElsevier, Amsterdam, 2006."},{"key":"2023033112553352384_j_anly-2021-0016_ref_014","doi-asserted-by":"crossref","unstructured":"O. A.  Ladyzhenskaya,\nThe Boundary Value Problems of Mathematical Physics,\nSpringer, New York, 1985.","DOI":"10.1007\/978-1-4757-4317-3"},{"key":"2023033112553352384_j_anly-2021-0016_ref_015","doi-asserted-by":"crossref","unstructured":"X. J.  Li and C. J.  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