Fractional Integrals and Derivatives to a Class of Functions

Name: Work Video:
Duration: 3 min 30 s
Description: In this paper, we apply fractional calculus to discussing a certain class of functions and obtain some interesting results. We examine the properties and applications of the Riemann fractional integral and derivative, and give the new definitions of left-sided fractional derivative and right-sided fractional derivative. Correspondingly, we discuss the properties and images of fractal function.
Qiang Xu
{'id': 'https://openalex.org/W2396296060', 'doi': None, 'title': 'Fractional Integrals and Derivatives to a Class of Functions', 'display_name': 'Fractional Integrals and Derivatives to a Class of Functions', 'publication_year': 2006, 'publication_date': '2006-12-15', 'ids': {'openalex': 'https://openalex.org/W2396296060', 'mag': '2396296060'}, 'language': 'en', 'primary_location': {'is_oa': False, 'landing_page_url': 'http://www.airitilibrary.com//Publication/Index?FirstID=10076573-200612-24-4-19-23-a', 'pdf_url': None, 'source': None, 'license': None, 'license_id': None, 'version': None, 'is_accepted': False, 'is_published': False}, 'type': 'article', 'type_crossref': 'journal-article', 'indexed_in': [], 'open_access': {'is_oa': False, 'oa_status': 'closed', 'oa_url': None, 'any_repository_has_fulltext': False}, 'authorships': [{'author_position': 'first', 'author': {'id': 'https://openalex.org/A5102379536', 'display_name': 'Qiang Xu', 'orcid': None}, 'institutions': [], 'countries': [], 'is_corresponding': True, 'raw_author_name': 'Qiang Xu', 'raw_affiliation_strings': [], 'affiliations': []}], 'institution_assertions': [], 'countries_distinct_count': 0, 'institutions_distinct_count': 0, 'corresponding_author_ids': ['https://openalex.org/A5102379536'], 'corresponding_institution_ids': [], 'apc_list': None, 'apc_paid': None, 'fwci': 0.0, 'has_fulltext': False, 'cited_by_count': 2, 'citation_normalized_percentile': {'value': 0.589511, 'is_in_top_1_percent': False, 'is_in_top_10_percent': False}, 'cited_by_percentile_year': {'min': 68, 'max': 72}, 'biblio': {'volume': '24', 'issue': '4', 'first_page': '19', 'last_page': '23'}, 'is_retracted': False, 'is_paratext': False, 'primary_topic': {'id': 'https://openalex.org/T10288', 'display_name': 'Fractional Differential Equations Solutions', 'score': 0.9983, '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': 0.9983, '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/T11428', 'display_name': 'Advanced Mathematical Identities', 'score': 0.9926, 'subfield': {'id': 'https://openalex.org/subfields/2602', 'display_name': 'Algebra and Number Theory'}, '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': 0.9924, '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': 0.5736035}], 'concepts': [{'id': 'https://openalex.org/C154249771', 'wikidata': 'https://www.wikidata.org/wiki/Q1339058', 'display_name': 'Fractional calculus', 'level': 2, 'score': 0.90591896}, {'id': 'https://openalex.org/C33923547', 'wikidata': 'https://www.wikidata.org/wiki/Q395', 'display_name': 'Mathematics', 'level': 0, 'score': 0.65661263}, {'id': 'https://openalex.org/C2777212361', 'wikidata': 'https://www.wikidata.org/wiki/Q5127848', 'display_name': 'Class (philosophy)', 'level': 2, 'score': 0.6199482}, {'id': 'https://openalex.org/C111771559', 'wikidata': 'https://www.wikidata.org/wiki/Q66295', 'display_name': 'Derivative (finance)', 'level': 2, 'score': 0.5736035}, {'id': 'https://openalex.org/C40636538', 'wikidata': 'https://www.wikidata.org/wiki/Q81392', 'display_name': 'Fractal', 'level': 2, 'score': 0.5643487}, {'id': 'https://openalex.org/C202444582', 'wikidata': 'https://www.wikidata.org/wiki/Q837863', 'display_name': 'Pure mathematics', 'level': 1, 'score': 0.47997996}, {'id': 'https://openalex.org/C2777686260', 'wikidata': 'https://www.wikidata.org/wiki/Q144037', 'display_name': 'Calculus (dental)', 'level': 2, 'score': 0.46926183}, {'id': 'https://openalex.org/C14036430', 'wikidata': 'https://www.wikidata.org/wiki/Q3736076', 'display_name': 'Function (biology)', 'level': 2, 'score': 0.4196238}, {'id': 'https://openalex.org/C134306372', 'wikidata': 'https://www.wikidata.org/wiki/Q7754', 'display_name': 'Mathematical analysis', 'level': 1, 'score': 0.4131104}, {'id': 'https://openalex.org/C28826006', 'wikidata': 'https://www.wikidata.org/wiki/Q33521', 'display_name': 'Applied mathematics', 'level': 1, 'score': 0.40634173}, {'id': 'https://openalex.org/C41008148', 'wikidata': 'https://www.wikidata.org/wiki/Q21198', 'display_name': 'Computer science', 'level': 0, 'score': 0.14213961}, {'id': 'https://openalex.org/C71924100', 'wikidata': 'https://www.wikidata.org/wiki/Q11190', 'display_name': 'Medicine', 'level': 0, 'score': 0.0}, {'id': 'https://openalex.org/C199343813', 'wikidata': 'https://www.wikidata.org/wiki/Q12128', 'display_name': 'Dentistry', 'level': 1, 'score': 0.0}, {'id': 'https://openalex.org/C154945302', 'wikidata': 'https://www.wikidata.org/wiki/Q11660', 'display_name': 'Artificial intelligence', 'level': 1, 'score': 0.0}, {'id': 'https://openalex.org/C78458016', 'wikidata': 'https://www.wikidata.org/wiki/Q840400', 'display_name': 'Evolutionary biology', '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}], 'mesh': [], 'locations_count': 1, 'locations': [{'is_oa': False, 'landing_page_url': 'http://www.airitilibrary.com//Publication/Index?FirstID=10076573-200612-24-4-19-23-a', 'pdf_url': None, 'source': None, 'license': None, 'license_id': None, 'version': None, 'is_accepted': False, 'is_published': False}], 'best_oa_location': None, 'sustainable_development_goals': [], 'grants': [], 'datasets': [], 'versions': [], 'referenced_works_count': 0, 'referenced_works': [], 'related_works': ['https://openalex.org/W3100161871', 'https://openalex.org/W3036210580', 'https://openalex.org/W3000525770', 'https://openalex.org/W2964287716', 'https://openalex.org/W2728137766', 'https://openalex.org/W2472840978', 'https://openalex.org/W2394099526', 'https://openalex.org/W2340479231', 'https://openalex.org/W2329139135', 'https://openalex.org/W2187932833', 'https://openalex.org/W2181978171', 'https://openalex.org/W2141536312', 'https://openalex.org/W2083432344', 'https://openalex.org/W2063190919', 'https://openalex.org/W2062595977', 'https://openalex.org/W2021368388', 'https://openalex.org/W1992972326', 'https://openalex.org/W1966208290', 'https://openalex.org/W1593649716', 'https://openalex.org/W1520610672'], 'abstract_inverted_index': {'In': [0], 'this': [1], 'paper,': [2], 'we': [3, 46], 'apply': [4], 'fractional': [5, 28, 39, 43], 'calculus': [6], 'to': [7], 'discussing': [8], 'a': [9], 'certain': [10], 'class': [11], 'of': [12, 25, 37, 52], 'functions': [13], 'and': [14, 23, 30, 32, 41, 50], 'obtain': [15], 'some': [16], 'interesting': [17], 'results.': [18], 'We': [19], 'examine': [20], 'the': [21, 26, 34, 48], 'properties': [22, 49], 'applications': [24], 'Riemann': [27], 'integral': [29], 'derivative,': [31], 'give': [33], 'new': [35], 'definitions': [36], 'left-sided': [38], 'derivative': [40], 'right-sided': [42], 'derivative.': [44], 'Correspondingly,': [45], 'discuss': [47], 'images': [51], 'fractal': [53], 'function.': [54]}, 'cited_by_api_url': 'https://api.openalex.org/works?filter=cites:W2396296060', 'counts_by_year': [{'year': 2022, 'cited_by_count': 1}, {'year': 2017, 'cited_by_count': 1}], 'updated_date': '2025-01-04T23:08:48.437976', 'created_date': '2016-06-24'}
Publication Information

Basic Information

Access and Citation

AI Researcher Chatbot

Primary Location

Authors

Topics

Keywords

Related Works
