Fractional-order Klein-Gordon nonlocal model for thermo-elasto-diffusion in porous medium

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Sur A., Alosaimi M., Singhal A., YAYLACI M., Das S.

Scientific Reports, vol.16, no.1, 2026 (SCI-Expanded, Scopus)

  • Publication Type: Article / Article
  • Volume: 16 Issue: 1
  • Publication Date: 2026
  • Doi Number: 10.1038/s41598-026-53535-y
  • Journal Name: Scientific Reports
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, BIOSIS, Chemical Abstracts Core, EMBASE, MEDLINE, Directory of Open Access Journals, Zoological Record, Academic Search Ultimate (EBSCO), Natural Science Collection (ProQuest), Biological Science Database (ProQuest), Biomedical Reference Collection: Corporate Edition (EBSCO), Health Research Premium Collection (ProQuest)
  • Keywords: Fractional-order derivative, Heat and mass transfer, Klein-Gordon operator, Modified Lord-Shulman model, Porous material
  • Open Archive Collection: AVESIS Open Access Collection
  • Recep Tayyip Erdoğan University Affiliated: Yes

Abstract

Classical heat conduction and thermoelastic theories are often inadequate for describing transport processes in modern micro and nano-scale materials, as they assume instantaneous propagation and neglect memory and nonlocal effects. This limitation becomes particularly important in applications such as semiconductor devices and porous structures subjected to rapid thermal and chemical loading. To address this issue, the present study develops a generalized thermo-elasto-diffusion model for porous medium by incorporating fractional-order heat conduction and Klein-Gordon-type nonlocal dynamics. The model extends the classical Lord–Shulman framework through a set of fractional-order modified models derived using an analogy with viscoelastic behavior, allowing both memory effects and spatial interactions to be captured through intrinsic time and length scales. Analytical solutions are obtained in the Laplace domain and numerically inverted using Zakian’s algorithm to evaluate the transient response of displacement, temperature, chemical potential, and stress fields. The results show that fractional-order parameters and nonlocal effects significantly influence wave propagation and heat transfer, especially near boundaries and in regions with strong microstructural interactions. Overall, the proposed framework provides a more realistic and physically consistent description of coupled thermo-mechanical processes, offering useful insights for the design and analysis of advanced porous and semiconductor materials under extreme conditions.