Existence and uniqueness of mild solution of time-fractional semilinear differential equations with a nonlocal final condition

Nguyen Huy Tuan; Tran Bao Ngoc; Le Nhat Huynh; Mokhtar Kirane

doi:10.1016/j.camwa.2018.11.007

$Existence and uniqueness of mild solution of time-fractional semilinear differential equations with a nonlocal final condition$

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Existence and uniqueness of mild solution of time-fractional semilinear differential equations with a nonlocal final condition

Nguyen Huy Tuan, Tran Bao Ngoc, Le Nhat Huynh and Mokhtar Kirane

Computers & mathematics with applications (1987), Vol.78(5), pp.1651-1668

01/09/2019

DOI: https://doi.org/10.1016/j.camwa.2018.11.007

Abstract

Fixed point theory

Fractional diffusion equation

Nonlocal problem

In this paper, we investigate a time-fractional semilinear differential equation with final nonlocal condition u(x,T)−(Gu)(x)=∑j=1mϑju(x,tj). Under some assumptions, we establish the existence and uniqueness of a mild solution in some suitable spaces of continuous functions. The results are based on some fixed point theorems. Two examples are presented to illustrate our results.

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Title: Existence and uniqueness of mild solution of time-fractional semilinear differential equations with a nonlocal final condition
Creators - without role: Nguyen Huy Tuan - Ton Duc Thang University
Tran Bao Ngoc - Nong Lam University Ho Chi Minh City
Le Nhat Huynh - Faculty of Mathematics and Computer Science, University of Science, Vietnam National University (VNU-HCMC), Ho Chi Minh city, Viet Nam
Mokhtar Kirane - University of La Rochelle
Publication Details: Computers & mathematics with applications (1987), Vol.78(5), pp.1651-1668
Publisher: Elsevier Ltd
Identifiers: 9934291908331
Academic Unit: King Abdulaziz University
Language: English
Resource Type: Journal article