A BOUNDARY VALUE PROBLEM WITH IMPULSIVE EFFECTS AND RIEMANN-LIOUVILLE TEMPERED FRACTIONAL DERIVATIVES

Hernán A. Cuti Gutierrez; Nemat Nyamoradi; César E. Torres Ledesma

doi:10.11948/20240068

2024 Volume 14 Issue 6

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Hernán A. Cuti Gutierrez, Nemat Nyamoradi, César E. Torres Ledesma. A BOUNDARY VALUE PROBLEM WITH IMPULSIVE EFFECTS AND RIEMANN-LIOUVILLE TEMPERED FRACTIONAL DERIVATIVES[J]. Journal of Applied Analysis & Computation, 2024, 14(6): 3496-3519. doi: 10.11948/20240068

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Hernán A. Cuti Gutierrez, Nemat Nyamoradi, César E. Torres Ledesma. A BOUNDARY VALUE PROBLEM WITH IMPULSIVE EFFECTS AND RIEMANN-LIOUVILLE TEMPERED FRACTIONAL DERIVATIVES[J]. Journal of Applied Analysis & Computation, 2024, 14(6): 3496-3519. doi: 10.11948/20240068

A BOUNDARY VALUE PROBLEM WITH IMPULSIVE EFFECTS AND RIEMANN-LIOUVILLE TEMPERED FRACTIONAL DERIVATIVES

1.
FCA Research Group, Departamento de Matemáticas, Instituto de Investigación en Matemáticas, FCFYM, Universidad Nacional de Trujillo, Av. Juan Pablo Ⅱ s/n. Trujillo-Perú, 13006, Trujillo, Peru
2.
Department of Mathematics, Faculty of Sciences, Razi University, 67149 Kermanshah, Iran

Author Bio: Email: hcuti@unitru.edu.pe(H. A. Cuti Gutierrez); Email: nyamoradi@razi.ac.ir(N. Nyamoradi)
Corresponding author: Email: ctl_576@yahoo.es(C. E. Torres Ledesma)

Abstract

Abstract

In this paper, we study a fractional impulsive differential equation with mixed tempered fractional derivatives. We justify some fundamental properties in the variational structure to fractional impulsive differential equations with the tempered fractional derivative operator. Finally, we study the existence of weak solutions with critical point theory and variational methods for the proposed problem. To prove the effectiveness of our main result, we investigate an interesting example.
- Riemann-Liouville and Caputo tempered fractional derivatives /
- impulsive effects /
- tempered fractional space of Sobolev type /
- variational methods
MSC: 26A33, 34A08, 34B15, 35J20

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References

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