The existence of a solution for nonlinear fractional differential equations where nonlinear term depends on the fractional and first order derivative of an unknown function-Reference-Cited by-同舟云学术

The existence of a solution for nonlinear fractional differential equations where nonlinear term depends on the fractional and first order derivative of an unknown function

Published:2023 Issue:12 Volume:37 Page:3871-3882
ISSN:0354-5180
Container-title:Filomat
language:en
Short-container-title:Filomat

Author:

Aleksic Suzana¹^ORCID,Cabada Alberto²,Dimitrijevic Sladjana¹^ORCID,Tomovic-Mladenovic Tatjana¹^ORCID

Affiliation:

1. University of Kragujevac, Faculty of Science, Kragujevac, Serbia

2. CITMAga, Santiago de Compostela, Galicia, Spain + Departamento de Estatística, Análise Matemática e Optimización, Facultade de Matemáticas, Universidade de Santiago de Compostela, Spain

Abstract

In this paper, we consider the existence of solutions of the nonlinear fractional differential equation boundary-value problem D?* u(t) = f (t, u(t), u?(t), CD?u(t)), 0 < t < 1, 1 < ? < 2, 0 < ? ? 1, u(0) = A, u(1) = Bu(?), where 0 < ? < 1, A ? 0, B? > 1, D?* is the modified Caputo fractional derivative of order ?, CD? is the Caputo fractional derivative of order ?, and f is a function in C([0, 1] ? R ? R ? R). Existence results for a solution are obtained. Two examples are presented to illustrate the results.

Publisher

National Library of Serbia

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