Bifurcation and Analytical Solutions of the Space-Fractional Stochastic Schrödinger Equation with White Noise
The qualitative theory for planar dynamical systems is used to study the bifurcation of the wave solutions for the space-fractional nonlinear Schrödinger equation with multiplicative white noise. Employing the first integral, we introduce some new wave solutions, assorted into periodic, solitary, an...
Saved in:
| Published in | Fractal and fractional Vol. 7; no. 2; p. 157 |
|---|---|
| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
Basel
MDPI AG
01.02.2023
|
| Subjects | |
| Online Access | Get full text |
Cover
Loading…
| Abstract | The qualitative theory for planar dynamical systems is used to study the bifurcation of the wave solutions for the space-fractional nonlinear Schrödinger equation with multiplicative white noise. Employing the first integral, we introduce some new wave solutions, assorted into periodic, solitary, and kink wave solutions. The dependence of the solutions on the initial conditions is investigated. Some solutions are clarified by the display of their 2D and 3D representations with varying levels of noise to show the influence of multiplicative white noise on the solutions. |
|---|---|
| AbstractList | The qualitative theory for planar dynamical systems is used to study the bifurcation of the wave solutions for the space-fractional nonlinear Schrödinger equation with multiplicative white noise. Employing the first integral, we introduce some new wave solutions, assorted into periodic, solitary, and kink wave solutions. The dependence of the solutions on the initial conditions is investigated. Some solutions are clarified by the display of their 2D and 3D representations with varying levels of noise to show the influence of multiplicative white noise on the solutions. |
| Audience | Academic |
| Author | Al Nuwairan, Muneerah |
| Author_xml | – sequence: 1 givenname: Muneerah orcidid: 0000-0001-9076-9945 surname: Al Nuwairan fullname: Al Nuwairan, Muneerah |
| BookMark | eNptkc1u1DAUha2qlShtn4CNJdYp_neyHKoWKlWwGBDL6MY_E4_SeGo7Qn0xXoAXw9NUiAX24lpH536-9nmLTuc4O4TeUXLNeUc--ASmwPRSNGGESn2CzpkkouGUktN_zm_QVc57QgjTHZdEn6P5Y_BLMlBCnDHMFm9mmJ5LMDDhbZyWo55x9LiMDm8PYFxzd7yoykdHiWaEXO14a8b0-5cN884lfPu0rMSfoYz4xxiKw19iyO4SnXmYsrt6rRfo-93tt5vPzcPXT_c3m4fGCKZLo52HQdqWEKDeOMm1o1x6ZcBYxroWaOu4IsxaBV4I1vmOU2GNJcNgu0HxC3S_cm2EfX9I4RHScx8h9C9CTLseUh17cr02Ug3KObDKCAJ1Wa6YpZ4LJlolK-v9yjqk-LS4XPp9XFJ9fu6Z1p1kHRdtdV2vrh1UaJh9LPWf6rbuMZiamA9V32jJKJVC8drA1waTYs7J-b9jUtIfg-3_Eyz_Az6CnZc |
| CitedBy_id | crossref_primary_10_3390_fractalfract7050372 crossref_primary_10_1007_s11082_024_06413_8 crossref_primary_10_3934_math_2024576 crossref_primary_10_3390_fractalfract8050298 crossref_primary_10_1515_math_2023_0143 crossref_primary_10_1088_1402_4896_ad21ca crossref_primary_10_3934_math_2024508 crossref_primary_10_1088_1402_4896_ad4f66 crossref_primary_10_3934_math_20231212 |
| Cites_doi | 10.1016/j.ijleo.2022.169831 10.1140/epjp/s13360-021-01957-0 10.1007/978-3-642-13694-8 10.1016/j.optcom.2004.06.047 10.1007/s13324-021-00477-5 10.1016/j.ijleo.2019.162948 10.1016/j.ijleo.2015.10.213 10.1016/j.joes.2021.07.006 10.3390/fractalfract7010016 10.1016/j.cam.2014.01.002 10.1007/s10955-018-2116-8 10.1016/S0375-9601(02)01516-5 10.1002/mma.8506 10.1088/1402-4896/ac0989 10.1103/PhysRevE.102.042212 10.3934/math.2022837 10.1016/j.physa.2019.123560 10.1016/j.ijleo.2019.163405 10.1016/j.chaos.2022.112548 10.1155/2021/9729905 10.1007/978-3-642-14003-7_11 10.1016/j.ijleo.2020.166223 10.1155/2022/3157217 10.1063/1.4705268 10.1142/S0219493702000443 10.1016/j.chaos.2021.111052 10.1007/s12346-021-00557-8 10.1155/2022/7188118 10.1016/j.physleta.2022.128268 10.1016/j.rinp.2020.102987 10.3233/FI-2019-1795 10.1016/j.jmaa.2008.03.061 10.3390/fractalfract6020108 10.1016/j.chaos.2019.109542 10.3390/sym14030597 |
| ContentType | Journal Article |
| Copyright | COPYRIGHT 2023 MDPI AG 2023 by the author. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License. |
| Copyright_xml | – notice: COPYRIGHT 2023 MDPI AG – notice: 2023 by the author. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License. |
| DBID | AAYXX CITATION 8FE 8FG ABJCF ABUWG AFKRA AZQEC BENPR BGLVJ CCPQU DWQXO HCIFZ L6V M7S PIMPY PQEST PQQKQ PQUKI PRINS PTHSS DOA |
| DOI | 10.3390/fractalfract7020157 |
| DatabaseName | CrossRef ProQuest SciTech Collection ProQuest Technology Collection Materials Science & Engineering Collection ProQuest Central (Alumni) ProQuest Central UK/Ireland ProQuest Central Essentials AUTh Library subscriptions: ProQuest Central Technology Collection ProQuest One Community College ProQuest Central SciTech Premium Collection (Proquest) (PQ_SDU_P3) ProQuest Engineering Collection ProQuest Engineering Database Access via ProQuest (Open Access) ProQuest One Academic Eastern Edition (DO NOT USE) ProQuest One Academic ProQuest One Academic UKI Edition ProQuest Central China Engineering Collection DOAJ Directory of Open Access Journals |
| DatabaseTitle | CrossRef Publicly Available Content Database Engineering Database Technology Collection ProQuest Central Essentials ProQuest One Academic Eastern Edition ProQuest Central (Alumni Edition) SciTech Premium Collection ProQuest One Community College ProQuest Technology Collection ProQuest SciTech Collection ProQuest Central China ProQuest Central ProQuest Engineering Collection ProQuest One Academic UKI Edition ProQuest Central Korea Materials Science & Engineering Collection ProQuest One Academic Engineering Collection |
| DatabaseTitleList | CrossRef Publicly Available Content Database |
| Database_xml | – sequence: 1 dbid: DOA name: DOAJ Directory of Open Access Journals url: https://www.doaj.org/ sourceTypes: Open Website – sequence: 2 dbid: 8FG name: ProQuest Technology Collection url: https://search.proquest.com/technologycollection1 sourceTypes: Aggregation Database |
| DeliveryMethod | fulltext_linktorsrc |
| EISSN | 2504-3110 |
| ExternalDocumentID | oai_doaj_org_article_7c56b6eead6c40aaaad362d1f3424865 A752115463 10_3390_fractalfract7020157 |
| GroupedDBID | 8FE 8FG AADQD AAYXX ABJCF ADBBV AFKRA AFZYC ALMA_UNASSIGNED_HOLDINGS BCNDV BENPR BGLVJ CCPQU CITATION GROUPED_DOAJ HCIFZ IAO ITC L6V M7S MODMG M~E OK1 PIMPY PROAC PTHSS ABUWG AZQEC DWQXO PQEST PQQKQ PQUKI PRINS |
| ID | FETCH-LOGICAL-c427t-7efab5d800a1fce537e135f6cacd2298a18e3602dd6af4429f9314dcd0bbd9b63 |
| IEDL.DBID | 8FG |
| ISSN | 2504-3110 |
| IngestDate | Tue Oct 22 15:10:27 EDT 2024 Thu Oct 10 16:01:45 EDT 2024 Fri Feb 02 04:16:22 EST 2024 Thu Sep 26 17:01:38 EDT 2024 |
| IsDoiOpenAccess | true |
| IsOpenAccess | true |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | 2 |
| Language | English |
| LinkModel | DirectLink |
| MergedId | FETCHMERGED-LOGICAL-c427t-7efab5d800a1fce537e135f6cacd2298a18e3602dd6af4429f9314dcd0bbd9b63 |
| ORCID | 0000-0001-9076-9945 |
| OpenAccessLink | https://www.proquest.com/docview/2779529348?pq-origsite=%requestingapplication% |
| PQID | 2779529348 |
| PQPubID | 2055410 |
| ParticipantIDs | doaj_primary_oai_doaj_org_article_7c56b6eead6c40aaaad362d1f3424865 proquest_journals_2779529348 gale_infotracacademiconefile_A752115463 crossref_primary_10_3390_fractalfract7020157 |
| PublicationCentury | 2000 |
| PublicationDate | 2023-02-01 |
| PublicationDateYYYYMMDD | 2023-02-01 |
| PublicationDate_xml | – month: 02 year: 2023 text: 2023-02-01 day: 01 |
| PublicationDecade | 2020 |
| PublicationPlace | Basel |
| PublicationPlace_xml | – name: Basel |
| PublicationTitle | Fractal and fractional |
| PublicationYear | 2023 |
| Publisher | MDPI AG |
| Publisher_xml | – name: MDPI AG |
| References | Wang (ref_18) 2022; 30 Wazwaz (ref_35) 2019; 192 Fan (ref_26) 2002; 305 Tanwar (ref_29) 2022; 21 ref_13 Cheemaa (ref_23) 2020; 17 (ref_17) 2019; 166 ref_10 ref_31 Akinyemi (ref_36) 2022; 7 Ghany (ref_4) 2012; 50 Ulutas (ref_3) 2021; 148 Elbrolosy (ref_33) 2021; 136 ref_39 ref_38 Han (ref_7) 2022; 163 Dong (ref_15) 2008; 344 Elbrolosy (ref_30) 2022; 2022 Seadawy (ref_24) 2020; 544 Khalil (ref_37) 2014; 264 Ramakrishnan (ref_20) 2020; 102 (ref_25) 2016; 127 Secer (ref_11) 2022; 268 (ref_14) 2018; 172 Li (ref_5) 2021; 2021 Han (ref_22) 2022; 7 Elmandouh (ref_34) 2021; 96 Imkeller (ref_9) 2002; 2 Khan (ref_2) 2020; 200 (ref_16) 2012; 53 Zayed (ref_12) 2022; 445 ref_28 Hassan (ref_32) 2022; 2022 Ma (ref_21) 2021; 11 ref_27 Biswas (ref_1) 2004; 239 Kim (ref_6) 2020; 131 ref_8 Jia (ref_19) 2021; 230 |
| References_xml | – volume: 268 start-page: 169831 year: 2022 ident: ref_11 article-title: Stochastic optical solitons with multiplicative white noise via Itô calculus publication-title: Optik doi: 10.1016/j.ijleo.2022.169831 contributor: fullname: Secer – volume: 136 start-page: 1 year: 2021 ident: ref_33 article-title: Dynamical behaviour of nondissipative double dispersive microstrain wave in the microstructured solids publication-title: Eur. Phys. J. Plus doi: 10.1140/epjp/s13360-021-01957-0 contributor: fullname: Elbrolosy – ident: ref_38 doi: 10.1007/978-3-642-13694-8 – volume: 239 start-page: 461 year: 2004 ident: ref_1 article-title: Stochastic perturbation of optical solitons in Schrödinger–Hirota equation publication-title: Opt. Commun. doi: 10.1016/j.optcom.2004.06.047 contributor: fullname: Biswas – volume: 11 start-page: 1 year: 2021 ident: ref_21 article-title: A binary Darboux transformation for multicomponent NLS equations and their reductions publication-title: Anal. Math. Phys. doi: 10.1007/s13324-021-00477-5 contributor: fullname: Ma – volume: 192 start-page: 162948 year: 2019 ident: ref_35 article-title: Bright and dark optical solitons for (2+ 1)-dimensional Schrödinger (NLS) equations in the anomalous dispersion regimes and the normal dispersive regimes publication-title: Optik doi: 10.1016/j.ijleo.2019.162948 contributor: fullname: Wazwaz – volume: 127 start-page: 1229 year: 2016 ident: ref_25 article-title: Constructing of exact solutions to the nonlinear Schrödinger equation (NLSE) with power-law nonlinearity by the Weierstrass elliptic function method publication-title: Optik doi: 10.1016/j.ijleo.2015.10.213 – volume: 7 start-page: 143 year: 2022 ident: ref_36 article-title: Analytical and approximate solutions of nonlinear Schrödinger equation with higher dimension in the anomalous dispersion regime publication-title: J. Ocean. Eng. Sci. doi: 10.1016/j.joes.2021.07.006 contributor: fullname: Akinyemi – ident: ref_10 doi: 10.3390/fractalfract7010016 – volume: 264 start-page: 65 year: 2014 ident: ref_37 article-title: A new definition of fractional derivative publication-title: J. Comput. Appl. Math. doi: 10.1016/j.cam.2014.01.002 contributor: fullname: Khalil – volume: 172 start-page: 1617 year: 2018 ident: ref_14 article-title: Path integral formulation of fractionally perturbed Lagrangian oscillators on fractal publication-title: J. Stat. Phys. doi: 10.1007/s10955-018-2116-8 – volume: 305 start-page: 383 year: 2002 ident: ref_26 article-title: Applications of the Jacobi elliptic function method to special-type nonlinear equations publication-title: Phys. Lett. A doi: 10.1016/S0375-9601(02)01516-5 contributor: fullname: Fan – ident: ref_31 doi: 10.1002/mma.8506 – volume: 96 start-page: 095214 year: 2021 ident: ref_34 article-title: Qualitative analysis and wave propagation of the nonlinear model for low-pass electrical transmission lines publication-title: Phys. Scr. doi: 10.1088/1402-4896/ac0989 contributor: fullname: Elmandouh – volume: 102 start-page: 042212 year: 2020 ident: ref_20 article-title: Nondegenerate solitons and their collisions in Manakov systems publication-title: Phys. Rev. E doi: 10.1103/PhysRevE.102.042212 contributor: fullname: Ramakrishnan – volume: 7 start-page: 15282 year: 2022 ident: ref_22 article-title: Optical solitons and single traveling wave solutions of Biswas-Arshed equation in birefringent fibers with the beta-time derivative publication-title: AIMS Math. doi: 10.3934/math.2022837 contributor: fullname: Han – volume: 544 start-page: 123560 year: 2020 ident: ref_24 article-title: Propagation of kink and anti-kink wave solitons for the nonlinear damped modified Korteweg–de Vries equation arising in ion-acoustic wave in an unmagnetized collisional dusty plasma publication-title: Phys. A Stat. Mech. Its Appl. doi: 10.1016/j.physa.2019.123560 contributor: fullname: Seadawy – ident: ref_39 – volume: 200 start-page: 163405 year: 2020 ident: ref_2 article-title: Stochastic perturbation of optical solitons having generalized anti-cubic non-linearity with band pass filters and multi-photon absorption publication-title: Optik doi: 10.1016/j.ijleo.2019.163405 contributor: fullname: Khan – volume: 163 start-page: 112548 year: 2022 ident: ref_7 article-title: Bifurcation and traveling wave solutions of stochastic Manakov model with multiplicative white noise in birefringent fibers publication-title: Chaos Solitons Fractals doi: 10.1016/j.chaos.2022.112548 contributor: fullname: Han – volume: 2021 start-page: 9729905 year: 2021 ident: ref_5 article-title: White Noise Functional Solutions for Wick-Type Stochastic Fractional Mixed KdV-mKdV Equation Using Extended-Expansion Method publication-title: Adv. Math. Phys. doi: 10.1155/2021/9729905 contributor: fullname: Li – ident: ref_13 doi: 10.1007/978-3-642-14003-7_11 – volume: 230 start-page: 166223 year: 2021 ident: ref_19 article-title: Solitons in PT symmetric Manakov system publication-title: Optik doi: 10.1016/j.ijleo.2020.166223 contributor: fullname: Jia – volume: 2022 start-page: 3157217 year: 2022 ident: ref_30 article-title: Dynamical behaviour of conformable time-fractional coupled Konno-Oono equation in magnetic field publication-title: Math. Probl. Eng. doi: 10.1155/2022/3157217 contributor: fullname: Elbrolosy – volume: 53 start-page: 042105 year: 2012 ident: ref_16 article-title: On the consistency of the solutions of the space fractional Schrödinger equation publication-title: J. Math. Phys. doi: 10.1063/1.4705268 – volume: 2 start-page: 311 year: 2002 ident: ref_9 article-title: Conceptual stochastic climate models publication-title: Stochastics Dyn. doi: 10.1142/S0219493702000443 contributor: fullname: Imkeller – volume: 148 start-page: 111052 year: 2021 ident: ref_3 article-title: Travelling wave and optical soliton solutions of the Wick-type stochastic NLSE with conformable derivatives publication-title: Chaos Solitons Fractals doi: 10.1016/j.chaos.2021.111052 contributor: fullname: Ulutas – ident: ref_8 – volume: 21 start-page: 1 year: 2022 ident: ref_29 article-title: Lie Symmetries and Dynamical Behavior of Soliton Solutions of KP-BBM Equation publication-title: Qual. Theory Dyn. Syst. doi: 10.1007/s12346-021-00557-8 contributor: fullname: Tanwar – volume: 50 start-page: 619 year: 2012 ident: ref_4 article-title: White noise functional solutions for Wick-type stochastic fractional KdV-Burgers-Kuramoto equations publication-title: Chin. J. Phys. contributor: fullname: Ghany – volume: 2022 start-page: 7188118 year: 2022 ident: ref_32 article-title: Bifurcation Analysis and Exact Wave Solutions for the Double-Chain Model of DNA publication-title: J. Math. doi: 10.1155/2022/7188118 contributor: fullname: Hassan – volume: 445 start-page: 128268 year: 2022 ident: ref_12 article-title: Dispersive optical solitons with Schrödinger–Hirota model having multiplicative white noise via Itô calculus publication-title: Phys. Lett. A doi: 10.1016/j.physleta.2022.128268 contributor: fullname: Zayed – volume: 17 start-page: 102987 year: 2020 ident: ref_23 article-title: Propagation of isolated waves of coupled nonlinear (2+ 1)-dimensional Maccari system in plasma physics publication-title: Results Phys. doi: 10.1016/j.rinp.2020.102987 contributor: fullname: Cheemaa – volume: 166 start-page: 87 year: 2019 ident: ref_17 article-title: Application of residual power series method for the solution of time-fractional Schrödinger equations in one-dimensional space publication-title: Fundam. Inform. doi: 10.3233/FI-2019-1795 – volume: 344 start-page: 1005 year: 2008 ident: ref_15 article-title: Space–time fractional Schrödinger equation with time-independent potentials publication-title: J. Math. Anal. Appl. doi: 10.1016/j.jmaa.2008.03.061 contributor: fullname: Dong – ident: ref_28 doi: 10.3390/fractalfract6020108 – volume: 30 start-page: 2240051 year: 2022 ident: ref_18 article-title: Numerical Solution of Traveling Waves in Chemical Kinetics: Time-Fractional Fishers Equations publication-title: Fractional contributor: fullname: Wang – volume: 131 start-page: 109542 year: 2020 ident: ref_6 article-title: Traveling wave solutions of some important Wick-type fractional stochastic nonlinear partial differential equations publication-title: Chaos Solitons Fractals doi: 10.1016/j.chaos.2019.109542 contributor: fullname: Kim – ident: ref_27 doi: 10.3390/sym14030597 |
| SSID | ssj0002793507 |
| Score | 2.3159602 |
| Snippet | The qualitative theory for planar dynamical systems is used to study the bifurcation of the wave solutions for the space-fractional nonlinear Schrödinger... |
| SourceID | doaj proquest gale crossref |
| SourceType | Open Website Aggregation Database |
| StartPage | 157 |
| SubjectTerms | bifurcation analysis Bifurcation theory Differential equations Dynamical systems Electric fields Equilibrium Exact solutions fractional derivatives Influence Initial conditions Ordinary differential equations Partial differential equations phase space Schrodinger equation stochastic shrödinger equation White noise |
| SummonAdditionalLinks | – databaseName: DOAJ Directory of Open Access Journals dbid: DOA link: http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwrV3LSh1BEG2Cq2xCxITcxEgvAtlkcPox_ViqeJFA3BjBXdNPVGRuch1_zR_Ij1nVPcpdGNw4m4GhGaqrprtO1XSdIuSbCdHronNno4idxDIZyzXrUj8YI6RKtsd651-n6uRc_rwYLjZafeGZsEYP3BS3r-OggsowYRVl7-FKsOcmVoTk0qjGXtrbjWDquv5OswKQTqMZEhDX7xcsOvI39aYBIzF0SBuuqDL2_29frs5m-Z68m1EiPWjSbZM3edwh4-FVuVu3FBv1Y6KVUKTmoulTdouuCgVMR88gFs7dct3qFnDEtIqXHlmZ6Vm8XP-7TzWhR4__NrJvihlZWvvl0dPV1W3-QM6Xx7-PTrq5XUIXJddTp3PxYUiAAD0rMQ9CZyaGoqKPiXNrPDNZqJ6npHyR4IeKFUymmPoQkg1KfCRb42rMnwgFn1648ULbwUuVhY05loBcdGVgJvAF-fGoOfensWI4iCZQ0e4ZRS_IIWr3aShSWtcHYGg3G9q9ZOgF-Y62cbjwJni5n-sHQGKksHIHGqRmyO6_ILuP5nPzirx1XMNkANtI8_k1pPlC3mLj-XZ-e5dsTeu7_BXgyRT26pf4AHOl55Y priority: 102 providerName: Directory of Open Access Journals |
| Title | Bifurcation and Analytical Solutions of the Space-Fractional Stochastic Schrödinger Equation with White Noise |
| URI | https://www.proquest.com/docview/2779529348 https://doaj.org/article/7c56b6eead6c40aaaad362d1f3424865 |
| Volume | 7 |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| link | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwfV3NbtQwELagvXBBoIJYKCsfkHohavwT2zmhLtptVakrRKnUm-X4h1ZCSZtNX40X4MWYcbJLD0AukRIrssZjz8yXmW8I-WAa73TSsai98IXEMpmaa1aEsjJGSBXqEuudL9bq7EqeX1fXE-C2mdIqt2diPqhD5xEjP-Za1xXYJmk-3d0X2DUK_65OLTSekn0GAzCly6xOdxgLB-UDf2ckGxIQ3R8nLD1yP_JNg6fE0Cw9MkiZt_9fp3M2OasX5PnkK9KTcXFfkiexPSDt4jY99CPQRl0baKYVyYg03WFctEsUPDt6CRFxLFb9WL2AI4bO3zjkZqaX_qb_9TNkWI8u70fKb4q4LM1d8-i6u93EV-Rqtfz2-ayYmiYUXnI9FDom11QB_EDHko-V0JGJKinvfOC8No6ZKFTJQ1AuSbBGqRZMBh_Kpgl1o8Rrstd2bXxDKFj2xI0TIHgnVRS1jz41yEiXKmYaPiMft5KzdyM3hoWYAgVt_yLoGVmgdHdDkdg6P-j673baJ1b7SjUqgn4rL0sHVwATG1gSkkujqhk5wrWxuP0G-LibqghgxkhkZU80zJohx_-MHG6Xz077cmP_aNHb_79-R55hY_kxP_uQ7A39Q3wP7sfQzLOOzcn-Yrn-8nWeg_jflCHhAQ |
| link.rule.ids | 315,783,787,867,2109,12778,21401,27937,27938,33386,33757,43613,43818,74370,74637 |
| linkProvider | ProQuest |
| linkToHtml | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwfV1Nb9QwELVge4ALKgLEQik-IHEhamI7tnOqutWuFmhXiLZSb5Y_aSWUtNn0r_EH-seYSbJLD0AukRIrssZjv_GL5w0hH7TzViUVs8pznwlMk6mYKrKQl1pzIUOVY77z6UouL8SXy_JyJNzW47HKzZrYL9Sh8ciRHzClqhKwSejDm9sMq0bh39WxhMZjsoNSVXpCdmbz1bfvW5aFgftBxDPIDXHY3x8kTD6yP_ubglipQGB6AEm9cv-_1ucedBa75NkYLdKjYXifk0exfkHq2XW6aweqjdo60F5YpOek6Zblok2iENvRM9gTx2zRDvkL2KJr_JVFdWZ65q_a-1-hJ_bo_HYQ_abIzNK-bh5dNdfr-JJcLObnx8tsLJuQecFUl6mYrCsDRIK2SD6WXMWCl0l66wNjlbaFjlzmLARpkwA8ShUvRPAhdy5UTvJXZFI3dXxNKGB7YtpyML0VMvLKR58catKlstCOTcmnjeXMzaCOYWBXgYY2fzH0lMzQutumKG3dP2jaH2acKUb5UjoZwcOlF7mFKwDIhiJxwYSW5ZR8xLExOAE7-Lgd8wigxyhlZY4U9LpAlf8p2dsMnxln5tr88aM3_3_9njxZnp-emJPPq69vyVMsMz-c1t4jk669i-8gGOnc_uhxvwGsQOLD |
| linkToPdf | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwfV1Lb9QwELaglRAXBALEQgEfkLgQbfyInZxQF3ZVXquKUqk3y_GjrYSSNpv-Nf4Af4wZx7twAHKJlFiRNQ_PIzPfEPKqbp3VUYeiccIVEttkGq5Z4cuqroVUvimx3_nLWh2dyo9n1Vmuf9rkssrtmZgOat87zJHPudZNBbZJ1vOYyyKO36_eXl0XOEEK_7TmcRq3yb6WSkAgtr9Yro-_7jIuHEQRvJ8JekhArD-P2Ihkv6ebBr-JoZH6wzwlFP9_ndXJAK3uk3vZc6SHE6sfkFuhe0i6xWW8Gaa0G7WdpwlkJOWn6S7jRftIwc-jJxAfh2I1TL0MuGLs3YVFpGZ64i6Gnz98SvLR5fUEAE4xS0vTDD267i834RE5XS2_vTsq8giFwkmux0KHaNvKg1doWXShEjowUUXlrPOcN7VldRCq5N4rGyXYptgIJr3zZdv6plXiMdnr-i48IRTsfOS1FcAGK1UQjQsutohPFytWt3xG3mwpZ64mpAwDEQYS2vyF0DOyQOruliLMdXrQD-cma43RrlKtCiDtysnSwuXB4HoWheSyVtWMvEbeGFTGET5uc08B7Bhhrcyhhl0zRPyfkYMt-0zW0o35LVNP___6JbkDwmY-f1h_ekbu4sT5qXD7gOyNw014Dn7J2L7IAvcL7WDm9w |
| openUrl | ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Bifurcation+and+Analytical+Solutions+of+the+Space-Fractional+Stochastic+Schr%C3%B6dinger+Equation+with+White+Noise&rft.jtitle=Fractal+and+fractional&rft.au=Al+Nuwairan%2C+Muneerah&rft.date=2023-02-01&rft.issn=2504-3110&rft.eissn=2504-3110&rft.volume=7&rft.issue=2&rft.spage=157&rft_id=info:doi/10.3390%2Ffractalfract7020157&rft.externalDBID=n%2Fa&rft.externalDocID=10_3390_fractalfract7020157 |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=2504-3110&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=2504-3110&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=2504-3110&client=summon |