Existence and uniqueness of solutions to higher order fractional partial differential equations with purely integral conditions-Reference-Cited by-同舟云学术

Existence and uniqueness of solutions to higher order fractional partial differential equations with purely integral conditions

Published:2022-10-26 Issue:1 Volume:43 Page:1-13
ISSN:0174-4747
Container-title:Analysis
language:en
Short-container-title:

Author:

Chergui Djamila¹,Merad Ahcene¹,Pinelas Sandra²^ORCID

Affiliation:

1. Department of Mathematics , Laboratory of Dynamical Systems and Control , University of Oum El Bouaghi , Oum El Bouaghi , Algeria

2. CINAMIL – Centro de Investigacão da Academia Militar , Academia Militar , Lisbo , Portugal

Abstract

Abstract In this paper, we prove the existence and uniqueness of Caputo time fractional pseudo-hyperbolic equations of higher order with purely nonlocal conditions of integral type. We use an a priori estimate method; the so-called energy inequalities method, based on some functional analysis tools, is developed for a Caputo time fractional of 2 ⁢ m

{2m}

-th and ( 2 ⁢ m + 1 )

{(2m+1)}

-th order and the density of the range of the operator generated by the considered problem. Using the Laplace transform and homotopy perturbation, we find a semi-analytical solution. Finally, we give some examples for illustration.

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,Numerical Analysis,Analysis

Link

https://www.degruyter.com/document/doi/10.1515/anly-2021-0016/pdf

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