On two backward problems with Dzherbashian-Nersesian operator

AIMS Mathematics

article

Anwar Ahmad¹  Dumitru Baleanu² 

[1] Department of Mathematics, COMSATS University Islamabad;Department of Mathematics, Cankaya University;Institute of Space Sciences;Department of Medical Research, China Medical University

关键词: Dzherbashian-Nersesian operator;    nonlocal boundary conditions;    backward problem;    Mittag-Leffler function;   

DOI  :  10.3934/math.2023043

学科分类：地球科学(综合)

来源: AIMS Press

【 摘 要 】

We investigate the initial-boundary value problems for a fourth-order differential equation within the powerful fractional Dzherbashian-Nersesian operator (FDNO). Boundary conditions considered in this manuscript are of the Samarskii-Ionkin type. The solutions obtained here are based on a series expansion using Riesz basis in a space corresponding to a non-self-adjoint spectral problem. Conditional to some regularity, consistency, alongside orthogonality dependence, the existence and uniqueness of the obtained solutions are exhibited by using Fourier method. Acquired results here are more general than those obtained by making use of conventional fractional operators such as fractional Riemann-Liouville derivative (FRLD), fractional Caputo derivative (FCD) and fractional Hilfer derivative (FHD).

【 授权许可】

CC BY