Get quick answers to your questions about the article from our AI researcher chatbot
{'id': 'https://openalex.org/W2963520255', 'doi': 'https://doi.org/10.28924/2291-8639-16-2018-83', 'title': 'A New Truncated M-Fractional Derivative Type Unifying Some Fractional Derivative Types with Classical Properties', 'display_name': 'A New Truncated M-Fractional Derivative Type Unifying Some Fractional Derivative Types with Classical Properties', 'publication_year': 2018, 'publication_date': '2018-01-01', 'ids': {'openalex': 'https://openalex.org/W2963520255', 'doi': 'https://doi.org/10.28924/2291-8639-16-2018-83', 'mag': '2963520255'}, 'language': 'en', 'primary_location': {'is_oa': True, 'landing_page_url': 'https://doi.org/10.28924/2291-8639-16-2018-83', 'pdf_url': 'http://www.etamaths.com/index.php/ijaa/article/download/1524/341', 'source': {'id': 'https://openalex.org/S2738108037', 'display_name': 'International Journal of Analysis and Applications', 'issn_l': '2291-8639', 'issn': ['2291-8639'], 'is_oa': True, 'is_in_doaj': True, 'is_core': False, 'host_organization': 'https://openalex.org/P4310312907', 'host_organization_name': 'Etamaths Publishing', 'host_organization_lineage': ['https://openalex.org/P4310312907'], 'host_organization_lineage_names': ['Etamaths Publishing'], 'type': 'journal'}, 'license': 'cc-by', 'license_id': 'https://openalex.org/licenses/cc-by', 'version': 'publishedVersion', 'is_accepted': True, 'is_published': True}, 'type': 'article', 'type_crossref': 'journal-article', 'indexed_in': ['crossref', 'doaj'], 'open_access': {'is_oa': True, 'oa_status': 'gold', 'oa_url': 'http://www.etamaths.com/index.php/ijaa/article/download/1524/341', 'any_repository_has_fulltext': True}, 'authorships': [{'author_position': 'first', 'author': {'id': 'https://openalex.org/A5066447517', 'display_name': 'J. Vanterler da C. Sousa', 'orcid': 'https://orcid.org/0000-0002-6986-948X'}, 'institutions': [{'id': 'https://openalex.org/I4210148978', 'display_name': 'Hospital de Clínicas da Unicamp', 'ror': 'https://ror.org/05g89bp20', 'country_code': 'BR', 'type': 'healthcare', 'lineage': ['https://openalex.org/I4210148978']}], 'countries': ['BR'], 'is_corresponding': False, 'raw_author_name': 'J. Vanterler da C. Sousa', 'raw_affiliation_strings': ['unicamp'], 'affiliations': [{'raw_affiliation_string': 'unicamp', 'institution_ids': ['https://openalex.org/I4210148978']}]}, {'author_position': 'last', 'author': {'id': 'https://openalex.org/A5072574433', 'display_name': 'E. Capelas de Oliveira', 'orcid': 'https://orcid.org/0000-0001-9661-0281'}, 'institutions': [{'id': 'https://openalex.org/I4210148978', 'display_name': 'Hospital de Clínicas da Unicamp', 'ror': 'https://ror.org/05g89bp20', 'country_code': 'BR', 'type': 'healthcare', 'lineage': ['https://openalex.org/I4210148978']}], 'countries': ['BR'], 'is_corresponding': False, 'raw_author_name': 'E. Capelas de Oliveira', 'raw_affiliation_strings': ['Unicamp'], 'affiliations': [{'raw_affiliation_string': 'Unicamp', 'institution_ids': ['https://openalex.org/I4210148978']}]}], 'institution_assertions': [], 'countries_distinct_count': 1, 'institutions_distinct_count': 1, 'corresponding_author_ids': [], 'corresponding_institution_ids': [], 'apc_list': {'value': 450, 'currency': 'USD', 'value_usd': 450, 'provenance': 'doaj'}, 'apc_paid': {'value': 450, 'currency': 'USD', 'value_usd': 450, 'provenance': 'doaj'}, 'fwci': 4.592, 'has_fulltext': True, 'fulltext_origin': 'pdf', 'cited_by_count': 150, 'citation_normalized_percentile': {'value': 0.999477, 'is_in_top_1_percent': True, 'is_in_top_10_percent': True}, 'cited_by_percentile_year': {'min': 98, 'max': 99}, 'biblio': {'volume': None, 'issue': None, 'first_page': None, 'last_page': None}, 'is_retracted': False, 'is_paratext': False, 'primary_topic': {'id': 'https://openalex.org/T10288', 'display_name': 'Fractional Differential Equations Solutions', 'score': 1.0, 'subfield': {'id': 'https://openalex.org/subfields/2611', 'display_name': 'Modeling and Simulation'}, 'field': {'id': 'https://openalex.org/fields/26', 'display_name': 'Mathematics'}, 'domain': {'id': 'https://openalex.org/domains/3', 'display_name': 'Physical Sciences'}}, 'topics': [{'id': 'https://openalex.org/T10288', 'display_name': 'Fractional Differential Equations Solutions', 'score': 1.0, 'subfield': {'id': 'https://openalex.org/subfields/2611', 'display_name': 'Modeling and Simulation'}, 'field': {'id': 'https://openalex.org/fields/26', 'display_name': 'Mathematics'}, 'domain': {'id': 'https://openalex.org/domains/3', 'display_name': 'Physical Sciences'}}, {'id': 'https://openalex.org/T10541', 'display_name': 'Nonlinear Differential Equations Analysis', 'score': 0.9896, 'subfield': {'id': 'https://openalex.org/subfields/2604', 'display_name': 'Applied Mathematics'}, 'field': {'id': 'https://openalex.org/fields/26', 'display_name': 'Mathematics'}, 'domain': {'id': 'https://openalex.org/domains/3', 'display_name': 'Physical Sciences'}}, {'id': 'https://openalex.org/T12661', 'display_name': 'Iterative Methods for Nonlinear Equations', 'score': 0.9893, 'subfield': {'id': 'https://openalex.org/subfields/2612', 'display_name': 'Numerical Analysis'}, 'field': {'id': 'https://openalex.org/fields/26', 'display_name': 'Mathematics'}, 'domain': {'id': 'https://openalex.org/domains/3', 'display_name': 'Physical Sciences'}}], 'keywords': [{'id': 'https://openalex.org/keywords/derivative', 'display_name': 'Derivative (finance)', 'score': 0.58989334}, {'id': 'https://openalex.org/keywords/beta', 'display_name': 'BETA (programming language)', 'score': 0.41632453}, {'id': 'https://openalex.org/keywords/fréchet-derivative', 'display_name': 'Fréchet derivative', 'score': 0.41270074}], 'concepts': [{'id': 'https://openalex.org/C154249771', 'wikidata': 'https://www.wikidata.org/wiki/Q1339058', 'display_name': 'Fractional calculus', 'level': 2, 'score': 0.9169649}, {'id': 'https://openalex.org/C33923547', 'wikidata': 'https://www.wikidata.org/wiki/Q395', 'display_name': 'Mathematics', 'level': 0, 'score': 0.7804302}, {'id': 'https://openalex.org/C202615002', 'wikidata': 'https://www.wikidata.org/wiki/Q783507', 'display_name': 'Differentiable function', 'level': 2, 'score': 0.6971995}, {'id': 'https://openalex.org/C2777299769', 'wikidata': 'https://www.wikidata.org/wiki/Q3707858', 'display_name': 'Type (biology)', 'level': 2, 'score': 0.6047076}, {'id': 'https://openalex.org/C111771559', 'wikidata': 'https://www.wikidata.org/wiki/Q66295', 'display_name': 'Derivative (finance)', 'level': 2, 'score': 0.58989334}, {'id': 'https://openalex.org/C184537036', 'wikidata': 'https://www.wikidata.org/wiki/Q14163503', 'display_name': 'Generalizations of the derivative', 'level': 3, 'score': 0.5862742}, {'id': 'https://openalex.org/C182306322', 'wikidata': 'https://www.wikidata.org/wiki/Q1779371', 'display_name': 'Order (exchange)', 'level': 2, 'score': 0.52296716}, {'id': 'https://openalex.org/C70915906', 'wikidata': 'https://www.wikidata.org/wiki/Q1058681', 'display_name': 'Differential operator', 'level': 2, 'score': 0.4785486}, {'id': 'https://openalex.org/C202444582', 'wikidata': 'https://www.wikidata.org/wiki/Q837863', 'display_name': 'Pure mathematics', 'level': 1, 'score': 0.44797626}, {'id': 'https://openalex.org/C97137487', 'wikidata': 'https://www.wikidata.org/wiki/Q729138', 'display_name': 'Integer (computer science)', 'level': 2, 'score': 0.43766037}, {'id': 'https://openalex.org/C2776174256', 'wikidata': 'https://www.wikidata.org/wiki/Q830842', 'display_name': 'BETA (programming language)', 'level': 2, 'score': 0.41632453}, {'id': 'https://openalex.org/C118335899', 'wikidata': 'https://www.wikidata.org/wiki/Q1305350', 'display_name': 'Fréchet derivative', 'level': 3, 'score': 0.41270074}, {'id': 'https://openalex.org/C134306372', 'wikidata': 'https://www.wikidata.org/wiki/Q7754', 'display_name': 'Mathematical analysis', 'level': 1, 'score': 0.33103696}, {'id': 'https://openalex.org/C132954091', 'wikidata': 'https://www.wikidata.org/wiki/Q194397', 'display_name': 'Banach space', 'level': 2, 'score': 0.06147924}, {'id': 'https://openalex.org/C18903297', 'wikidata': 'https://www.wikidata.org/wiki/Q7150', 'display_name': 'Ecology', 'level': 1, 'score': 0.0}, {'id': 'https://openalex.org/C106159729', 'wikidata': 'https://www.wikidata.org/wiki/Q2294553', 'display_name': 'Financial economics', 'level': 1, 'score': 0.0}, {'id': 'https://openalex.org/C162324750', 'wikidata': 'https://www.wikidata.org/wiki/Q8134', 'display_name': 'Economics', 'level': 0, 'score': 0.0}, {'id': 'https://openalex.org/C86803240', 'wikidata': 'https://www.wikidata.org/wiki/Q420', 'display_name': 'Biology', 'level': 0, 'score': 0.0}, {'id': 'https://openalex.org/C10138342', 'wikidata': 'https://www.wikidata.org/wiki/Q43015', 'display_name': 'Finance', 'level': 1, 'score': 0.0}, {'id': 'https://openalex.org/C41008148', 'wikidata': 'https://www.wikidata.org/wiki/Q21198', 'display_name': 'Computer science', 'level': 0, 'score': 0.0}, {'id': 'https://openalex.org/C199360897', 'wikidata': 'https://www.wikidata.org/wiki/Q9143', 'display_name': 'Programming language', 'level': 1, 'score': 0.0}], 'mesh': [], 'locations_count': 4, 'locations': [{'is_oa': True, 'landing_page_url': 'https://doi.org/10.28924/2291-8639-16-2018-83', 'pdf_url': 'http://www.etamaths.com/index.php/ijaa/article/download/1524/341', 'source': {'id': 'https://openalex.org/S2738108037', 'display_name': 'International Journal of Analysis and Applications', 'issn_l': '2291-8639', 'issn': ['2291-8639'], 'is_oa': True, 'is_in_doaj': True, 'is_core': False, 'host_organization': 'https://openalex.org/P4310312907', 'host_organization_name': 'Etamaths Publishing', 'host_organization_lineage': ['https://openalex.org/P4310312907'], 'host_organization_lineage_names': ['Etamaths Publishing'], 'type': 'journal'}, 'license': 'cc-by', 'license_id': 'https://openalex.org/licenses/cc-by', 'version': 'publishedVersion', 'is_accepted': True, 'is_published': True}, {'is_oa': False, 'landing_page_url': 'https://doaj.org/article/5ad91eb2a1b94348aeafbc8ef0902e70', 'pdf_url': None, 'source': {'id': 'https://openalex.org/S4306401280', 'display_name': 'DOAJ (DOAJ: Directory of Open Access Journals)', 'issn_l': None, 'issn': None, 'is_oa': True, 'is_in_doaj': False, 'is_core': False, 'host_organization': None, 'host_organization_name': None, 'host_organization_lineage': [], 'host_organization_lineage_names': [], 'type': 'repository'}, 'license': None, 'license_id': None, 'version': None, 'is_accepted': False, 'is_published': False}, {'is_oa': False, 'landing_page_url': 'https://doaj.org/article/c64c0e39c581455494eae10d3ae07a30', 'pdf_url': None, 'source': {'id': 'https://openalex.org/S4306401280', 'display_name': 'DOAJ (DOAJ: Directory of Open Access Journals)', 'issn_l': None, 'issn': None, 'is_oa': True, 'is_in_doaj': False, 'is_core': False, 'host_organization': None, 'host_organization_name': None, 'host_organization_lineage': [], 'host_organization_lineage_names': [], 'type': 'repository'}, 'license': None, 'license_id': None, 'version': None, 'is_accepted': False, 'is_published': False}, {'is_oa': True, 'landing_page_url': 'https://arxiv.org/abs/1704.08187', 'pdf_url': 'https://arxiv.org/pdf/1704.08187', 'source': {'id': 'https://openalex.org/S4306400194', 'display_name': 'arXiv (Cornell University)', 'issn_l': None, 'issn': None, 'is_oa': True, 'is_in_doaj': False, 'is_core': False, 'host_organization': 'https://openalex.org/I205783295', 'host_organization_name': 'Cornell University', 'host_organization_lineage': ['https://openalex.org/I205783295'], 'host_organization_lineage_names': ['Cornell University'], 'type': 'repository'}, 'license': None, 'license_id': None, 'version': 'submittedVersion', 'is_accepted': False, 'is_published': False}], 'best_oa_location': {'is_oa': True, 'landing_page_url': 'https://doi.org/10.28924/2291-8639-16-2018-83', 'pdf_url': 'http://www.etamaths.com/index.php/ijaa/article/download/1524/341', 'source': {'id': 'https://openalex.org/S2738108037', 'display_name': 'International Journal of Analysis and Applications', 'issn_l': '2291-8639', 'issn': ['2291-8639'], 'is_oa': True, 'is_in_doaj': True, 'is_core': False, 'host_organization': 'https://openalex.org/P4310312907', 'host_organization_name': 'Etamaths Publishing', 'host_organization_lineage': ['https://openalex.org/P4310312907'], 'host_organization_lineage_names': ['Etamaths Publishing'], 'type': 'journal'}, 'license': 'cc-by', 'license_id': 'https://openalex.org/licenses/cc-by', 'version': 'publishedVersion', 'is_accepted': True, 'is_published': True}, 'sustainable_development_goals': [], 'grants': [], 'datasets': [], 'versions': [], 'referenced_works_count': 13, 'referenced_works': ['https://openalex.org/W1584611818', 'https://openalex.org/W1585552811', 'https://openalex.org/W2006205876', 'https://openalex.org/W2063067239', 'https://openalex.org/W2129879686', 'https://openalex.org/W2469685909', 'https://openalex.org/W2561797461', 'https://openalex.org/W2565956535', 'https://openalex.org/W2611107039', 'https://openalex.org/W2787959293', 'https://openalex.org/W3150837077', 'https://openalex.org/W4254896208', 'https://openalex.org/W4293200410'], 'related_works': ['https://openalex.org/W4382753044', 'https://openalex.org/W4375959275', 'https://openalex.org/W4300257736', 'https://openalex.org/W4298858041', 'https://openalex.org/W4206562187', 'https://openalex.org/W2963305955', 'https://openalex.org/W2930126963', 'https://openalex.org/W2610382785', 'https://openalex.org/W2097846334', 'https://openalex.org/W2089892488'], 'abstract_inverted_index': {'We': [0, 44, 109], 'introduce': [1], 'a': [2, 120, 146], 'truncated': [3, 89, 98], '$M$-fractional': [4, 41, 99, 141], 'derivative': [5, 39, 63, 100], 'type': [6, 101], 'for': [7], '$\\alpha$-differentiable': [8], 'functions': [9], 'that': [10, 66, 81], 'generalizes': [11], 'four': [12], 'other': [13], 'fractional': [14, 31, 34, 38, 114], 'derivatives': [15], 'types': [16], 'recently': [17], 'introduced': [18], 'by': [19, 50], 'Khalil': [20], 'et': [21, 26], 'al.,': [22, 27], 'Katugampola': [23], 'and': [24, 40, 72, 144], 'Sousa': [25], 'the': [28, 54, 59, 62, 77, 82, 88, 103, 106, 112, 123, 136, 140], 'so-called': [29], 'conformable': [30], 'derivative,': [32, 35, 42], 'alternative': [33, 37], 'generalized': [36], 'respectively.': [43], 'denote': [45], 'this': [46, 97], 'new': [47], 'differential': [48], 'operator': [49], '$_{i}\\mathscr{D}_{M}^{\\alpha,\\beta': [51], '}$,': [52], 'where': [53], 'parameter': [55], '$\\alpha$,': [56], 'associated': [57], 'with': [58, 92], 'order': [60], 'of': [61, 96, 105, 139], 'is': [64, 76], 'such': [65], '$': [67, 73, 75], '0': [68], '<\\alpha<1': [69], '$,': [70], '$\\beta>0$': [71], 'M': [74], 'notation': [78], 'to': [79, 84], 'designate': [80], 'function': [83, 91], 'be': [85, 127], 'derived': [86], 'involves': [87], 'Mittag-Leffler': [90], 'one': [93], 'parameter.The': [94], 'definition': [95], 'satisfies': [102], 'properties': [104], 'integer-order': [107], 'calculus.': [108], 'also': [110], 'present,': [111], 'respective': [113], 'integral': [115], 'from': [116], 'which': [117, 125], 'emerges,': [118], 'as': [119, 129], 'natural': [121], 'consequence,': [122], 'result,': [124], 'can': [126], 'interpreted': [128], 'an': [130], 'inverse': [131], 'property.': [132], 'Finally,': [133], 'we': [134], 'obtain': [135], 'analytical': [137], 'solution': [138], 'heat': [142], 'equation': [143], 'present': [145], 'graphical': [147], 'analysis.': [148]}, 'cited_by_api_url': 'https://api.openalex.org/works?filter=cites:W2963520255', 'counts_by_year': [{'year': 2024, 'cited_by_count': 22}, {'year': 2023, 'cited_by_count': 18}, {'year': 2022, 'cited_by_count': 14}, {'year': 2021, 'cited_by_count': 17}, {'year': 2020, 'cited_by_count': 8}, {'year': 2019, 'cited_by_count': 9}, {'year': 2018, 'cited_by_count': 5}, {'year': 2017, 'cited_by_count': 1}], 'updated_date': '2024-12-28T04:03:16.717242', 'created_date': '2019-07-30'}