Green's functions and existence of solutions of nonlinear fractional implicit difference equations with Dirichlet boundary conditions

• Autorzy: Cabada Alberto , Dimitrov Nikolay D. , Jonnalagadda Jagan Mohan

Identyfikatory

DOI

10.7494/OpMath.2024.44.2.167

• Języki publikacji: EN

Abstrakty

EN

This article is devoted to deduce the expression of the Green’s function related to a general constant coefficients fractional difference equation coupled to Dirichlet conditions. In this case, due to the points where some of the fractional operators are applied, we are in presence of an implicit fractional difference equation. So, due to such a property, it is more complicated to calculate and manage the expression of the Green’s function than in the explicit case studied in a previous work of the authors. Contrary to the explicit case, where it is shown that the Green’s function is constructed as finite sums, the Green’s function constructed here is an infinite series. This fact makes necessary to impose more restrictive assumptions on the parameters that appear in the equation. The expression of the Green’s function will be deduced from the Laplace transform on the time scales of the integers. We point out that, despite the implicit character of the considered equation, we can have an explicit expression of the solution by means of the expression of the Green’s function. These two facts are not incompatible. Even more, this method allows us to have an explicit expression of the solution of an implicit problem. Finally, we prove two existence results for nonlinear problems, via suitable fixed point theorems.

Słowa kluczowe

EN

fractional difference; Dirichlet conditions; Green’s function; existence of solutions

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2024
• Tom: Vol. 44, no. 2
• Strony: 167--195
• Opis fizyczny: Bibliogr. 24 poz.

Twórcy

autor

Cabada Alberto

• CITMAga, 15782, Santiago de Compostela, Galicia, Spain
• Departamento de Estatística, Análise Matemática e Optimización, Facultade de Matemáticas, Universidade de Santiago de Compostela, Santiago de Compostela, Galicia, Spain

• https://orcid.org/0000-0003-1488-935X

autor

Dimitrov Nikolay D.

• University of Ruse, Department of Mathematics, Studentska 8 Str., Ruse, Bulgaria

• https://orcid.org/0000-0002-3185-1532

autor

Jonnalagadda Jagan Mohan

• Birla Institute of Technology and Science Pilani, Department of Mathematics, Hyderabad – 500078, Telangana, India

• https://orcid.org/0000-0002-1310-8323

Bibliografia

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Uwagi

Opracowanie rekordu ze środków MEiN, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2022-2023)