On multi-step methods for singular fractional q-integro-differential equations

The objective of this paper is to investigate, by applying the standard Caputo fractional -derivative of order , the existence of solutions for the singular fractional -integro-differential equation , under some boundary conditions where is singular at some point , on a time scale , for where and ....

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Published inOpen mathematics (Warsaw, Poland) Vol. 19; no. 1; pp. 1378 - 1405
Main Authors Hajiseyedazizi, Sayyedeh Narges, Samei, Mohammad Esmael, Alzabut, Jehad, Chu, Yu-ming
Format Journal Article
LanguageEnglish
Published Warsaw De Gruyter 31.12.2021
De Gruyter Poland
Subjects
34A08
34B16
39A13
Algorithms
Boundary conditions
Continuity (mathematics)
Differential equations
integro-differential equation
multi-step methods
q-integro-differential equation
singularity
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Summary:The objective of this paper is to investigate, by applying the standard Caputo fractional -derivative of order , the existence of solutions for the singular fractional -integro-differential equation , under some boundary conditions where is singular at some point , on a time scale , for where and . We consider the compact map and avail the Lebesgue dominated theorem for finding solutions of the addressed problem. Besides, we prove the main results in context of completely continuous functions. Our attention is concentrated on fractional multi-step methods of both implicit and explicit type, for which sufficient existence conditions are investigated. Finally, we present some examples involving graphs, tables and algorithms to illustrate the validity of our theoretical findings.
ISSN:2391-5455
2391-5455
DOI:10.1515/math-2021-0093