A generalization of truncated M-fractional derivative and applications to fractional differential equations
In this paper, our aim is to generalize the truncated M-fractional derivative which was recently introduced [Sousa and de Oliveira, A new truncated M-fractional derivative type unifying some fractional derivative types with classical properties, Inter. of Jour. Analy. and Appl., 16 (1), 83–96, 2018]...
Saved in:
| Published in | Applied mathematics and nonlinear sciences Vol. 5; no. 1; pp. 171 - 188 |
|---|---|
| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Beirut
Sciendo
01.01.2020
De Gruyter Poland |
| Subjects | |
| Online Access | Get full text |
Cover
Loading…
| Abstract | In this paper, our aim is to generalize the truncated M-fractional derivative which was recently introduced [Sousa and de Oliveira, A new truncated M-fractional derivative type unifying some fractional derivative types with classical properties, Inter. of Jour. Analy. and Appl., 16 (1), 83–96, 2018]. To do that, we used generalized M-series, which has a more general form than Mittag-Leffler and hypergeometric functions. We called this generalization as truncated ℳ-series fractional derivative. This new derivative generalizes several fractional derivatives and satisfies important properties of the integer-order derivatives. Finally, we obtain the analytical solutions of some ℳ-series fractional differential equations. |
|---|---|
| AbstractList | In this paper, our aim is to generalize the truncated M-fractional derivative which was recently introduced [Sousa and de Oliveira, A new truncated M-fractional derivative type unifying some fractional derivative types with classical properties, Inter. of Jour. Analy. and Appl., 16 (1), 83–96, 2018]. To do that, we used generalized M-series, which has a more general form than Mittag-Leffler and hypergeometric functions. We called this generalization as truncated ℳ-series fractional derivative. This new derivative generalizes several fractional derivatives and satisfies important properties of the integer-order derivatives. Finally, we obtain the analytical solutions of some ℳ-series fractional differential equations. |
| Author | İlhan, Esin Kıymaz, İ. Onur |
| Author_xml | – sequence: 1 givenname: Esin surname: İlhan fullname: İlhan, Esin organization: Mucur Vocational School, Ahi Evran University, 40500, Kırşehir, Turkey – sequence: 2 givenname: İ. Onur surname: Kıymaz fullname: Kıymaz, İ. Onur email: iokiymaz@ahievran.edu.tr organization: Dept. of Mathematics, Faculty of Science, Ahi Evran University, 40100, Kırşehir, Turkey |
| BookMark | eNp9kE1LxDAQhoMoqKs_wFvAc9dM0qa7F0HEL1C86DnMJhOJ1nZNUkV_ve2uoAh6ymR4nuHl3WWbbdcSYwcgprKsZ0f43KapFFJMYSqEAL3BdmRZlsVMV3rzx7zN9lN6HBCpQGktd9jTCX-gliI24QNz6FreeZ5j31rM5PhN4SPacY8NdxTD6wC9EsfWcVwum2BXUuK54z_J4D1FanMYPvTSr6E9tuWxSbT_9U7Y_fnZ3ellcX17cXV6cl1YVUMuPPpKlxXZkqjW5IDE3IOHmQSNslbeIeiFW6B1TtcLi0JUcuErNffzEVETdri-u4zdS08pm8euj0OuZBTMQSottRqoek3Z2KUUyRsb8ipojhgaA8KM5ZqxXDOWa8Csyh1M-GUuY3jG-P6vc7x23rDJFB09xP59GL6j_elWADWoT1DElwQ |
| CitedBy_id | crossref_primary_10_1007_s11063_022_10809_6 crossref_primary_10_1186_s13662_020_03093_y crossref_primary_10_1140_epjs_s11734_022_00457_1 crossref_primary_10_32604_cmc_2022_032087 crossref_primary_10_1016_j_rinp_2023_106272 crossref_primary_10_1186_s13660_021_02735_3 crossref_primary_10_1016_j_chaos_2021_111674 crossref_primary_10_3934_math_2021648 crossref_primary_10_3390_axioms11050234 crossref_primary_10_1007_s11082_023_05899_y crossref_primary_10_2478_fcds_2021_0017 crossref_primary_10_1140_epjp_s13360_022_02525_w crossref_primary_10_1002_mma_9228 crossref_primary_10_3934_math_2021251 crossref_primary_10_32604_cmc_2022_021462 crossref_primary_10_1002_num_22662 crossref_primary_10_1007_s40819_020_00911_5 crossref_primary_10_1016_j_asoc_2022_109975 crossref_primary_10_1140_epjp_s13360_024_05423_5 crossref_primary_10_1142_S0218348X21502509 crossref_primary_10_2478_amns_2022_2_0159 crossref_primary_10_3390_fractalfract6060333 crossref_primary_10_1007_s44196_021_00009_w crossref_primary_10_1007_s40819_020_00923_1 crossref_primary_10_1016_j_aej_2020_08_044 crossref_primary_10_1016_j_rinp_2022_105198 crossref_primary_10_1007_s11082_025_08093_4 crossref_primary_10_1186_s13662_020_02951_z crossref_primary_10_3934_mbe_2022030 crossref_primary_10_1007_s40995_020_00986_1 crossref_primary_10_1088_1402_4896_ac7174 crossref_primary_10_1109_ACCESS_2022_3217663 crossref_primary_10_1142_S0218348X22402678 crossref_primary_10_3390_axioms12060519 crossref_primary_10_1142_S0218348X22401107 crossref_primary_10_1155_2021_6640086 crossref_primary_10_1080_10236198_2021_1976770 crossref_primary_10_1016_j_rinp_2020_103330 crossref_primary_10_1016_j_joes_2021_09_006 crossref_primary_10_3390_sym15020361 crossref_primary_10_3390_fractalfract5010006 crossref_primary_10_1016_j_sciaf_2020_e00594 crossref_primary_10_32604_cmc_2022_028921 crossref_primary_10_1063_5_0085737 crossref_primary_10_3390_fractalfract7050350 crossref_primary_10_2478_amns_2021_1_00006 crossref_primary_10_32604_cmes_2021_014988 crossref_primary_10_3390_math10152719 crossref_primary_10_3390_fractalfract6100604 crossref_primary_10_1007_s11042_022_14270_4 crossref_primary_10_1007_s11082_022_03627_6 crossref_primary_10_1002_mma_7151 crossref_primary_10_1016_j_aej_2021_01_004 crossref_primary_10_3390_math11040975 crossref_primary_10_3390_sym13071159 crossref_primary_10_3934_math_20221101 crossref_primary_10_3934_math_2023126 crossref_primary_10_1140_epjp_s13360_022_02421_3 crossref_primary_10_2478_amns_2021_2_00093 crossref_primary_10_3934_mbe_2021268 crossref_primary_10_1016_j_padiff_2024_101011 crossref_primary_10_3390_fractalfract5040160 crossref_primary_10_3390_sym13122428 crossref_primary_10_11948_20230418 crossref_primary_10_3390_fractalfract8100593 crossref_primary_10_3390_axioms12060592 crossref_primary_10_1088_1402_4896_ad1e45 crossref_primary_10_1142_S0217984921502651 crossref_primary_10_1155_2021_5554280 crossref_primary_10_1016_j_rinp_2023_106776 crossref_primary_10_1016_j_rinp_2023_106777 crossref_primary_10_47000_tjmcs_999775 crossref_primary_10_1007_s11082_023_05528_8 crossref_primary_10_1142_S0218348X22402411 crossref_primary_10_3934_mmc_2022019 crossref_primary_10_1016_j_csite_2021_101193 crossref_primary_10_1155_2020_8819183 crossref_primary_10_1155_2021_2536720 crossref_primary_10_32604_cmc_2023_030996 crossref_primary_10_2478_amns_2022_2_0131 crossref_primary_10_3390_fractalfract6100553 crossref_primary_10_1002_mma_7022 crossref_primary_10_1016_j_aej_2023_12_052 crossref_primary_10_1016_j_padiff_2024_101001 crossref_primary_10_1007_s40096_021_00403_7 crossref_primary_10_1007_s11082_024_06663_6 crossref_primary_10_1016_j_aej_2021_04_020 crossref_primary_10_1016_j_rinp_2020_103551 crossref_primary_10_1142_S0217984921506284 crossref_primary_10_1155_2020_5063271 crossref_primary_10_1186_s13662_020_02822_7 crossref_primary_10_1002_mma_10807 crossref_primary_10_3390_fractalfract6050231 crossref_primary_10_1016_j_aej_2021_02_037 crossref_primary_10_1016_j_aej_2022_02_054 crossref_primary_10_11948_20230124 crossref_primary_10_1007_s00521_022_06998_9 crossref_primary_10_1371_journal_pone_0265064 crossref_primary_10_1142_S0218348X21400235 crossref_primary_10_32604_cmc_2023_031352 crossref_primary_10_1080_00207160_2021_1929940 crossref_primary_10_32604_cmc_2022_029432 crossref_primary_10_1155_2021_1426212 crossref_primary_10_1142_S0217984923500598 crossref_primary_10_3390_math11040835 crossref_primary_10_1142_S0218348X22400564 crossref_primary_10_2478_amns_2022_2_0182 crossref_primary_10_1186_s13662_021_03612_5 crossref_primary_10_1007_s40995_020_00976_3 crossref_primary_10_3390_axioms11090449 crossref_primary_10_1155_2022_3774123 crossref_primary_10_1016_j_imu_2022_101105 crossref_primary_10_32604_cmc_2022_027523 crossref_primary_10_1002_num_22622 crossref_primary_10_1002_num_22587 crossref_primary_10_1051_mmnp_2020046 crossref_primary_10_1016_j_chaos_2020_110096 crossref_primary_10_32604_cmc_2023_029046 crossref_primary_10_1140_epjp_s13360_022_02869_3 crossref_primary_10_32604_cmc_2023_032950 crossref_primary_10_32604_cmc_2023_034699 crossref_primary_10_2478_amns_2023_1_00438 crossref_primary_10_1155_2022_1724221 crossref_primary_10_1155_2023_9720612 crossref_primary_10_3390_fractalfract5040277 crossref_primary_10_3390_fractalfract6040184 crossref_primary_10_1155_2020_8815363 crossref_primary_10_1016_j_aej_2020_10_055 crossref_primary_10_3390_fractalfract7010063 crossref_primary_10_1007_s11182_022_02497_5 crossref_primary_10_1007_s00500_022_07359_3 crossref_primary_10_1186_s13662_021_03286_z crossref_primary_10_1016_j_chaos_2020_110417 crossref_primary_10_1016_j_rinp_2021_105137 crossref_primary_10_2478_amns_2023_1_00032 crossref_primary_10_1007_s00521_024_10361_5 crossref_primary_10_1007_s40995_020_01042_8 crossref_primary_10_1155_2022_8419403 crossref_primary_10_1016_j_aej_2020_08_034 crossref_primary_10_1007_s12530_021_09413_1 crossref_primary_10_2478_amns_2022_2_0161 crossref_primary_10_3390_math11173792 crossref_primary_10_1007_s11082_023_05103_1 crossref_primary_10_3934_mbe_2022037 crossref_primary_10_1186_s13662_020_02831_6 crossref_primary_10_3390_sym14112322 crossref_primary_10_1080_00207160_2023_2248286 crossref_primary_10_1080_02286203_2023_2249640 crossref_primary_10_1109_ACCESS_2024_3417647 crossref_primary_10_1142_S0217984921502171 crossref_primary_10_1142_S0217984921505679 crossref_primary_10_1007_s40819_024_01727_3 crossref_primary_10_1016_j_chaos_2021_111347 crossref_primary_10_1016_j_cjph_2021_01_012 crossref_primary_10_1007_s11063_022_10963_x crossref_primary_10_1155_2021_5568492 crossref_primary_10_1186_s13662_020_02935_z crossref_primary_10_2478_amns_2022_2_0177 crossref_primary_10_1016_j_arabjc_2022_104493 crossref_primary_10_1002_mma_7178 crossref_primary_10_2478_amns_2022_2_0180 crossref_primary_10_2478_amns_2022_2_0181 crossref_primary_10_1016_j_rinp_2023_106602 crossref_primary_10_32604_cmc_2022_029437 crossref_primary_10_32604_cmc_2023_034362 crossref_primary_10_1016_j_rinp_2021_104104 crossref_primary_10_1063_5_0163991 crossref_primary_10_1016_j_arabjc_2023_104706 |
| Cites_doi | 10.22436/jnsa.009.06.14 10.1016/j.chaos.2017.03.022 10.1140/epjp/i2017-11293-3 10.18576/pfda/020204 10.2298/TSCI151224222Y 10.1186/s13662-018-1612-0 10.22436/jnsa.008.05.01 10.1515/ausm-2015-0009 10.1007/978-981-10-4337-6_11 10.1007/s00009-017-1046-z 10.1007/s40314-018-0639-x 10.2298/TSCI160111018A 10.1007/BF02403202 10.1007/978-3-662-43930-2 10.1016/j.cam.2014.01.002 |
| ContentType | Journal Article |
| Copyright | 2020. This work is published under http://creativecommons.org/licenses/by/4.0 (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License. |
| Copyright_xml | – notice: 2020. This work is published under http://creativecommons.org/licenses/by/4.0 (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License. |
| DBID | AAYXX CITATION ABUWG AFKRA AZQEC BENPR CCPQU DWQXO PHGZM PHGZT PIMPY PKEHL PQEST PQQKQ PQUKI PRINS |
| DOI | 10.2478/amns.2020.1.00016 |
| DatabaseName | CrossRef ProQuest Central (Alumni) ProQuest Central UK/Ireland ProQuest Central Essentials ProQuest Central ProQuest One Community College ProQuest Central ProQuest Central Premium ProQuest One Academic (New) Publicly Available Content Database ProQuest One Academic Middle East (New) ProQuest One Academic Eastern Edition (DO NOT USE) ProQuest One Academic ProQuest One Academic UKI Edition ProQuest Central China |
| DatabaseTitle | CrossRef Publicly Available Content Database ProQuest One Academic Middle East (New) ProQuest Central Essentials ProQuest One Academic Eastern Edition ProQuest Central (Alumni Edition) ProQuest One Community College ProQuest Central China ProQuest Central ProQuest One Academic UKI Edition ProQuest Central Korea ProQuest Central (New) ProQuest One Academic ProQuest One Academic (New) |
| DatabaseTitleList | CrossRef Publicly Available Content Database |
| Database_xml | – sequence: 1 dbid: BENPR name: ProQuest Central url: https://www.proquest.com/central sourceTypes: Aggregation Database |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Applied Sciences |
| EISSN | 2444-8656 |
| EndPage | 188 |
| ExternalDocumentID | 10_2478_amns_2020_1_00016 10_2478_amns_2020_1_0001651171 |
| GroupedDBID | 9WM AATOW ABFKT ADBLJ AFKRA AHGSO ALMA_UNASSIGNED_HOLDINGS AMVHM ARCSS BENPR CCPQU EBS M~E OK1 PHGZM PHGZT PIMPY QD8 SLJYH AAYXX CITATION ABUWG AZQEC DWQXO PKEHL PQEST PQQKQ PQUKI PRINS |
| ID | FETCH-LOGICAL-c371t-faf5645ec4ee76ed1e09f1f18216a273fda16bdbacdd67bca0052bf539f9216a3 |
| IEDL.DBID | BENPR |
| ISSN | 2444-8656 |
| IngestDate | Mon Jun 30 11:42:33 EDT 2025 Thu Apr 24 23:10:02 EDT 2025 Tue Jul 01 03:14:25 EDT 2025 Thu Jul 10 10:36:51 EDT 2025 |
| IsDoiOpenAccess | true |
| IsOpenAccess | true |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | 1 |
| Language | English |
| License | This work is licensed under the Creative Commons Attribution 4.0 International License. http://creativecommons.org/licenses/by/4.0 |
| LinkModel | DirectLink |
| MergedId | FETCHMERGED-LOGICAL-c371t-faf5645ec4ee76ed1e09f1f18216a273fda16bdbacdd67bca0052bf539f9216a3 |
| Notes | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 |
| OpenAccessLink | https://www.proquest.com/docview/3191236263?pq-origsite=%requestingapplication% |
| PQID | 3191236263 |
| PQPubID | 6761185 |
| PageCount | 18 |
| ParticipantIDs | proquest_journals_3191236263 crossref_citationtrail_10_2478_amns_2020_1_00016 crossref_primary_10_2478_amns_2020_1_00016 walterdegruyter_journals_10_2478_amns_2020_1_0001651171 |
| ProviderPackageCode | CITATION AAYXX |
| PublicationCentury | 2000 |
| PublicationDate | 2020-01-01 |
| PublicationDateYYYYMMDD | 2020-01-01 |
| PublicationDate_xml | – month: 01 year: 2020 text: 2020-01-01 day: 01 |
| PublicationDecade | 2020 |
| PublicationPlace | Beirut |
| PublicationPlace_xml | – name: Beirut |
| PublicationTitle | Applied mathematics and nonlinear sciences |
| PublicationYear | 2020 |
| Publisher | Sciendo De Gruyter Poland |
| Publisher_xml | – name: Sciendo – name: De Gruyter Poland |
| References | 2025012704083001056_j_amns.2020.1.00016_ref_033_w2aab3b7d814b1b6b1ab2b1c33Aa 2025012704083001056_j_amns.2020.1.00016_ref_008_w2aab3b7d814b1b6b1ab2b1b8Aa 2025012704083001056_j_amns.2020.1.00016_ref_003_w2aab3b7d814b1b6b1ab2b1b3Aa 2025012704083001056_j_amns.2020.1.00016_ref_024_w2aab3b7d814b1b6b1ab2b1c24Aa 2025012704083001056_j_amns.2020.1.00016_ref_029_w2aab3b7d814b1b6b1ab2b1c29Aa 2025012704083001056_j_amns.2020.1.00016_ref_023_w2aab3b7d814b1b6b1ab2b1c23Aa 2025012704083001056_j_amns.2020.1.00016_ref_014_w2aab3b7d814b1b6b1ab2b1c14Aa 2025012704083001056_j_amns.2020.1.00016_ref_019_w2aab3b7d814b1b6b1ab2b1c19Aa 2025012704083001056_j_amns.2020.1.00016_ref_004_w2aab3b7d814b1b6b1ab2b1b4Aa 2025012704083001056_j_amns.2020.1.00016_ref_009_w2aab3b7d814b1b6b1ab2b1b9Aa 2025012704083001056_j_amns.2020.1.00016_ref_002_w2aab3b7d814b1b6b1ab2b1b2Aa 2025012704083001056_j_amns.2020.1.00016_ref_032_w2aab3b7d814b1b6b1ab2b1c32Aa 2025012704083001056_j_amns.2020.1.00016_ref_028_w2aab3b7d814b1b6b1ab2b1c28Aa 2025012704083001056_j_amns.2020.1.00016_ref_031_w2aab3b7d814b1b6b1ab2b1c31Aa 2025012704083001056_j_amns.2020.1.00016_ref_022_w2aab3b7d814b1b6b1ab2b1c22Aa 2025012704083001056_j_amns.2020.1.00016_ref_027_w2aab3b7d814b1b6b1ab2b1c27Aa 2025012704083001056_j_amns.2020.1.00016_ref_018_w2aab3b7d814b1b6b1ab2b1c18Aa 2025012704083001056_j_amns.2020.1.00016_ref_005_w2aab3b7d814b1b6b1ab2b1b5Aa 2025012704083001056_j_amns.2020.1.00016_ref_013_w2aab3b7d814b1b6b1ab2b1c13Aa 2025012704083001056_j_amns.2020.1.00016_ref_017_w2aab3b7d814b1b6b1ab2b1c17Aa 2025012704083001056_j_amns.2020.1.00016_ref_012_w2aab3b7d814b1b6b1ab2b1c12Aa 2025012704083001056_j_amns.2020.1.00016_ref_001_w2aab3b7d814b1b6b1ab2b1b1Aa 2025012704083001056_j_amns.2020.1.00016_ref_006_w2aab3b7d814b1b6b1ab2b1b6Aa 2025012704083001056_j_amns.2020.1.00016_ref_030_w2aab3b7d814b1b6b1ab2b1c30Aa 2025012704083001056_j_amns.2020.1.00016_ref_021_w2aab3b7d814b1b6b1ab2b1c21Aa 2025012704083001056_j_amns.2020.1.00016_ref_026_w2aab3b7d814b1b6b1ab2b1c26Aa 2025012704083001056_j_amns.2020.1.00016_ref_025_w2aab3b7d814b1b6b1ab2b1c25Aa 2025012704083001056_j_amns.2020.1.00016_ref_020_w2aab3b7d814b1b6b1ab2b1c20Aa 2025012704083001056_j_amns.2020.1.00016_ref_011_w2aab3b7d814b1b6b1ab2b1c11Aa 2025012704083001056_j_amns.2020.1.00016_ref_016_w2aab3b7d814b1b6b1ab2b1c16Aa 2025012704083001056_j_amns.2020.1.00016_ref_010_w2aab3b7d814b1b6b1ab2b1c10Aa 2025012704083001056_j_amns.2020.1.00016_ref_015_w2aab3b7d814b1b6b1ab2b1c15Aa 2025012704083001056_j_amns.2020.1.00016_ref_007_w2aab3b7d814b1b6b1ab2b1b7Aa |
| References_xml | – ident: 2025012704083001056_j_amns.2020.1.00016_ref_006_w2aab3b7d814b1b6b1ab2b1b6Aa – ident: 2025012704083001056_j_amns.2020.1.00016_ref_027_w2aab3b7d814b1b6b1ab2b1c27Aa – ident: 2025012704083001056_j_amns.2020.1.00016_ref_009_w2aab3b7d814b1b6b1ab2b1b9Aa – ident: 2025012704083001056_j_amns.2020.1.00016_ref_018_w2aab3b7d814b1b6b1ab2b1c18Aa doi: 10.22436/jnsa.009.06.14 – ident: 2025012704083001056_j_amns.2020.1.00016_ref_001_w2aab3b7d814b1b6b1ab2b1b1Aa – ident: 2025012704083001056_j_amns.2020.1.00016_ref_020_w2aab3b7d814b1b6b1ab2b1c20Aa – ident: 2025012704083001056_j_amns.2020.1.00016_ref_005_w2aab3b7d814b1b6b1ab2b1b5Aa doi: 10.1016/j.chaos.2017.03.022 – ident: 2025012704083001056_j_amns.2020.1.00016_ref_013_w2aab3b7d814b1b6b1ab2b1c13Aa doi: 10.1140/epjp/i2017-11293-3 – ident: 2025012704083001056_j_amns.2020.1.00016_ref_015_w2aab3b7d814b1b6b1ab2b1c15Aa doi: 10.18576/pfda/020204 – ident: 2025012704083001056_j_amns.2020.1.00016_ref_033_w2aab3b7d814b1b6b1ab2b1c33Aa doi: 10.2298/TSCI151224222Y – ident: 2025012704083001056_j_amns.2020.1.00016_ref_016_w2aab3b7d814b1b6b1ab2b1c16Aa – ident: 2025012704083001056_j_amns.2020.1.00016_ref_011_w2aab3b7d814b1b6b1ab2b1c11Aa doi: 10.1186/s13662-018-1612-0 – ident: 2025012704083001056_j_amns.2020.1.00016_ref_003_w2aab3b7d814b1b6b1ab2b1b3Aa doi: 10.22436/jnsa.008.05.01 – ident: 2025012704083001056_j_amns.2020.1.00016_ref_008_w2aab3b7d814b1b6b1ab2b1b8Aa – ident: 2025012704083001056_j_amns.2020.1.00016_ref_007_w2aab3b7d814b1b6b1ab2b1b7Aa doi: 10.1515/ausm-2015-0009 – ident: 2025012704083001056_j_amns.2020.1.00016_ref_024_w2aab3b7d814b1b6b1ab2b1c24Aa – ident: 2025012704083001056_j_amns.2020.1.00016_ref_019_w2aab3b7d814b1b6b1ab2b1c19Aa doi: 10.1007/978-981-10-4337-6_11 – ident: 2025012704083001056_j_amns.2020.1.00016_ref_021_w2aab3b7d814b1b6b1ab2b1c21Aa – ident: 2025012704083001056_j_amns.2020.1.00016_ref_028_w2aab3b7d814b1b6b1ab2b1c28Aa doi: 10.1007/s00009-017-1046-z – ident: 2025012704083001056_j_amns.2020.1.00016_ref_010_w2aab3b7d814b1b6b1ab2b1c10Aa – ident: 2025012704083001056_j_amns.2020.1.00016_ref_022_w2aab3b7d814b1b6b1ab2b1c22Aa – ident: 2025012704083001056_j_amns.2020.1.00016_ref_002_w2aab3b7d814b1b6b1ab2b1b2Aa – ident: 2025012704083001056_j_amns.2020.1.00016_ref_030_w2aab3b7d814b1b6b1ab2b1c30Aa doi: 10.1007/s40314-018-0639-x – ident: 2025012704083001056_j_amns.2020.1.00016_ref_004_w2aab3b7d814b1b6b1ab2b1b4Aa doi: 10.2298/TSCI160111018A – ident: 2025012704083001056_j_amns.2020.1.00016_ref_032_w2aab3b7d814b1b6b1ab2b1c32Aa doi: 10.1007/BF02403202 – ident: 2025012704083001056_j_amns.2020.1.00016_ref_012_w2aab3b7d814b1b6b1ab2b1c12Aa doi: 10.1007/978-3-662-43930-2 – ident: 2025012704083001056_j_amns.2020.1.00016_ref_025_w2aab3b7d814b1b6b1ab2b1c25Aa – ident: 2025012704083001056_j_amns.2020.1.00016_ref_017_w2aab3b7d814b1b6b1ab2b1c17Aa doi: 10.1016/j.cam.2014.01.002 – ident: 2025012704083001056_j_amns.2020.1.00016_ref_026_w2aab3b7d814b1b6b1ab2b1c26Aa – ident: 2025012704083001056_j_amns.2020.1.00016_ref_023_w2aab3b7d814b1b6b1ab2b1c23Aa – ident: 2025012704083001056_j_amns.2020.1.00016_ref_029_w2aab3b7d814b1b6b1ab2b1c29Aa – ident: 2025012704083001056_j_amns.2020.1.00016_ref_031_w2aab3b7d814b1b6b1ab2b1c31Aa – ident: 2025012704083001056_j_amns.2020.1.00016_ref_014_w2aab3b7d814b1b6b1ab2b1c14Aa |
| SSID | ssj0002313662 |
| Score | 2.5146468 |
| Snippet | In this paper, our aim is to generalize the truncated M-fractional derivative which was recently introduced [Sousa and de Oliveira, A new truncated... |
| SourceID | proquest crossref walterdegruyter |
| SourceType | Aggregation Database Enrichment Source Index Database Publisher |
| StartPage | 171 |
| SubjectTerms | 26A33 33E20 34A08 alternative fractional derivative conformable fractional derivative M-series Truncated M-fractional derivative |
| Title | A generalization of truncated M-fractional derivative and applications to fractional differential equations |
| URI | https://www.degruyter.com/doi/10.2478/amns.2020.1.00016 https://www.proquest.com/docview/3191236263 |
| Volume | 5 |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| link | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwfV07T8MwELagLCzlLcpLHpiQDHEeTjKhgooQUhFCVLBFjn1moKSPBBD_nnPi0oIE-9lDvvPd57v4O0KOPQg4xDJiyqQpC5XnMUzDHkshjFKQSQjG1iH7t-J6EN48RU-u4Fa63ypnMbEO1HqkbI38DF3FCoX4IjgfT5idGmW7q26ExjJZwRCcJC2yctG7vbv_rrIgewmE8Jt2ph_GyZl8LaxKt4_B4rQmPD8T0pxltj_qfrWG5-nbZzXrj9Zp52qdtB1fpN0G4A2yBMUmWXPckbqTWW6Rly59bhSk3cNKOjK0mr5ZzVc07DMzbZ4w4GYave69FvymstB0sYdNqxFdtHTjUzAMDClMGlnwcpsMrnoPl9fMDVJgKoh5xYw0VjQGVAgQC9AcvNRwg1cLLiTyF6MlF7nOpdJaxLmStlicmyhITWpNgh3SKkYF7BJqjNSJtiJnkQ4jlafg5zk3ke8B-mTid4g3-5qZcirjdtjFMMPbhgUgswBkFoCM151v0SEn30vGjcTGf8YHM4gyd9rKbO4bHRL_gm1u9eeeyDljvvf_xvtk1S5pii8HpIUAwiHSkSo_wqj62D9ynvcFlr3kbA |
| linkProvider | ProQuest |
| linkToHtml | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwtV1NT9wwEB3R5dBe6LfYloIP5YLkEjuJszlUFS2gpbCrqgKJW-rYYw5AFnZDEX-qv7HjxGGhUrlxH8_BM555nrHfAHyMMBaY6ZQbl-c8MVHEKQ1HPMckzVEPEnS-Djkaq-FR8v04PV6AP91fGP-ssouJTaC2E-Nr5JvkKp4oRKr4y8Ul91OjfHe1G6HRusU-3lzTlW32eW-b7Lsu5e7O4bchD1MFuIkzUXOnnWdQQZMgZgqtwCh3whHOFkpTMndWC1XaUhtrVVYa7SunpUvj3OVeJCa9T2AxiVUke7D4dWf84-dtVYfQUqyUbNunMskGm_q88qzgkoLTpwZg3U-Ac1S7dN30xy2eTK9u6q4f26S53RewFPAp22od6iUsYPUKngesykIkmL2G0y120jJWh4-cbOJYPb3yHLMkOOJu2n6ZIGWWvPx3QzDOdGXZ3Z45qyfsrmQY10Jh54zhZUtDPnsDR4-yxW-hV00qXAbmnLYD60nVUpukpsxRlqVwqYyQzsBA9iHqdrMwgdXcD9c4K-h24w1QeAMU3gCFaDrtqg8bt0suWkqPh4RXOhMV4XTPirkv9iH7x2xzqf_qJIybiXcPK16Dp8PD0UFxsDfefw_P_PK28LMCPTImfiAoVJerwf8Y_Hpsl_8Lm2YiSA |
| linkToPdf | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwtV3PTxQxFH5BSIwX_AGGRdQe4EJSmXZm2u3Bw0ZcFxAwURJuQ2f6ykGchd1Bwp_jf-rrTBfQqAcT7q9N0--9vq997VeA9QRTgdrmvPLG8KxKEk5pOOEGs9yg7Wfowznk_oEaHWW7x_nxHPyYvYVp133XViu3zp1vrypnur9lv9VBXFtSjL9peUq8R7mH11e0S5u-3dkmSDekHL7_8m7E40cCvEq1aLi3PoimYJUhaoVOYGK88ESthbKUv72zQpWutJVzSpeVDYelpc9T400wSanfB7CgcyMpiBYGow-fD28OcoggpUrJrmL657H-mvNuieziVVsSd3g6ubxuZiXYNrMNn8BipKRs0PnQU5jD-hk8jvSUxeCfLsHXATvtRKrj20029qyZXAZZWTLc537SvZKgzhw59vdWU5zZ2rG7ZXLWjNldy_hDC600ZwwvOuXx6TIc3csUP4f5elzjCjDvreu7oKOWuyyvSoOyLIXPZYLk9n3Zg2Q2m0UVhczDfxpnBW1oAgBFAKAIABSiLa6rHmzeNDnvVDz-Zbw2g6iIAT0taKUKOjVSpT3Qv8F2a_XXPonWarH63y1fw8NP28Pi487B3gt4lOpwBy7jQq3BPMGML4kXNeWr6JkMTu47GH4CDpgi9A |
| 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=A+generalization+of+truncated+M-fractional+derivative+and+applications+to+fractional+differential+equations&rft.jtitle=Applied+mathematics+and+nonlinear+sciences&rft.au=%C4%B0lhan%2C+Esin&rft.au=K%C4%B1ymaz%2C+%C4%B0.+Onur&rft.date=2020-01-01&rft.pub=Sciendo&rft.eissn=2444-8656&rft.volume=5&rft.issue=1&rft.spage=171&rft.epage=188&rft_id=info:doi/10.2478%2Famns.2020.1.00016&rft.externalDBID=n%2Fa&rft.externalDocID=10_2478_amns_2020_1_0001651171 |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=2444-8656&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=2444-8656&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=2444-8656&client=summon |