FRINK Linked Data Fragments server

Matches in SemOpenAlex for { <https://semopenalex.org/work/W4366204509> ?p ?o ?g. }

• W4366204509 endingPage "988" @default.
• W4366204509 startingPage "962" @default.
• W4366204509 abstract "Abstract We prove existence of solutions, and particularly positive solutions, of initial value problems (IVPs) for nonlinear fractional differential equations involving the Caputo differential operator of order $$alpha in (0,1)$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mrow> <mml:mi>α</mml:mi> <mml:mo>∈</mml:mo> <mml:mo>(</mml:mo> <mml:mn>0</mml:mn> <mml:mo>,</mml:mo> <mml:mn>1</mml:mn> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> . One novelty in this paper is that it is not assumed that f is continuous but that it satisfies an $$L^{p}$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:msup> <mml:mi>L</mml:mi> <mml:mi>p</mml:mi> </mml:msup> </mml:math> -Carathéodory condition for some $$p>frac{1}{alpha }$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mrow> <mml:mi>p</mml:mi> <mml:mo>></mml:mo> <mml:mfrac> <mml:mn>1</mml:mn> <mml:mi>α</mml:mi> </mml:mfrac> </mml:mrow> </mml:math> (detailed definitions are given in the paper). We prove existence on an interval [0, T ] in cases where T can be arbitrarily large, called global solutions. The necessary a priori bounds are found using a new version of the Bihari inequality that we prove here. We show that global solutions exist when f ( t , u ) grows at most linearly in u , and also in some cases when the growth is faster than linear. We give examples of the new results for some fractional differential equations with nonlinearities related to some that occur in combustion theory. We also discuss in detail the often used alternative definition of Caputo fractional derivative and we show that it has severe disadvantages which restricts its use. In particular we prove that there is a necessary condition in order that solutions of the IVP can exist with this definition, which has often been overlooked in the literature." @default.
• W4366204509 created "2023-04-19" @default.
• W4366204509 creator A5024664440 @default.
• W4366204509 creator A5028548638 @default.
• W4366204509 date "2023-04-17" @default.
• W4366204509 modified "2023-10-04" @default.
• W4366204509 title "A new Bihari inequality and initial value problems of first order fractional differential equations" @default.
• W4366204509 cites W1560060148 @default.
• W4366204509 cites W1967903843 @default.
• W4366204509 cites W1975670568 @default.
• W4366204509 cites W1979540139 @default.
• W4366204509 cites W2013843940 @default.
• W4366204509 cites W2031840763 @default.
• W4366204509 cites W2064612733 @default.
• W4366204509 cites W2066947701 @default.
• W4366204509 cites W2067578821 @default.
• W4366204509 cites W2079131035 @default.
• W4366204509 cites W2080797270 @default.
• W4366204509 cites W2109416477 @default.
• W4366204509 cites W2134837756 @default.
• W4366204509 cites W2220568363 @default.
• W4366204509 cites W2526302245 @default.
• W4366204509 cites W2610240197 @default.
• W4366204509 cites W2791630794 @default.
• W4366204509 cites W2900439483 @default.
• W4366204509 cites W3004221154 @default.
• W4366204509 cites W3024986605 @default.
• W4366204509 cites W3035997017 @default.
• W4366204509 cites W3118821734 @default.
• W4366204509 cites W3204248146 @default.
• W4366204509 cites W3208696785 @default.
• W4366204509 cites W3210265809 @default.
• W4366204509 cites W4206409304 @default.
• W4366204509 cites W4247953052 @default.
• W4366204509 cites W426962928 @default.
• W4366204509 doi "https://doi.org/10.1007/s13540-023-00152-5" @default.
• W4366204509 hasPubMedId "https://pubmed.ncbi.nlm.nih.gov/37251655" @default.
• W4366204509 hasPublicationYear "2023" @default.
• W4366204509 type Work @default.
• W4366204509 citedByCount "1" @default.
• W4366204509 countsByYear W43662045092023 @default.
• W4366204509 crossrefType "journal-article" @default.
• W4366204509 hasAuthorship W4366204509A5024664440 @default.
• W4366204509 hasAuthorship W4366204509A5028548638 @default.
• W4366204509 hasBestOaLocation W43662045091 @default.
• W4366204509 hasConcept C11413529 @default.
• W4366204509 hasConcept C33923547 @default.
• W4366204509 hasConceptScore W4366204509C11413529 @default.
• W4366204509 hasConceptScore W4366204509C33923547 @default.
• W4366204509 hasFunder F4320334593 @default.
• W4366204509 hasIssue "3" @default.
• W4366204509 hasLocation W43662045091 @default.
• W4366204509 hasLocation W43662045092 @default.
• W4366204509 hasLocation W43662045093 @default.
• W4366204509 hasLocation W43662045094 @default.
• W4366204509 hasOpenAccess W4366204509 @default.
• W4366204509 hasPrimaryLocation W43662045091 @default.
• W4366204509 hasRelatedWork W1587224694 @default.
• W4366204509 hasRelatedWork W1979597421 @default.
• W4366204509 hasRelatedWork W2007980826 @default.
• W4366204509 hasRelatedWork W2061531152 @default.
• W4366204509 hasRelatedWork W2077600819 @default.
• W4366204509 hasRelatedWork W2142036596 @default.
• W4366204509 hasRelatedWork W2911598644 @default.
• W4366204509 hasRelatedWork W3002753104 @default.
• W4366204509 hasRelatedWork W4225152035 @default.
• W4366204509 hasRelatedWork W4245490552 @default.
• W4366204509 hasVolume "26" @default.
• W4366204509 isParatext "false" @default.
• W4366204509 isRetracted "false" @default.
• W4366204509 workType "article" @default.