OICC Press Journal of Solid Mechanics 2008-7683 17 3 2025 11 24 Thermomechanical interaction in photothermoelastic with fractional order derivatives and hyperbolic two temperature 301 320 10.60664/jsm.2025.3021770 EN Supriya Chopra Maharishi Markandeshwar University Mullana, Ambala, Haryana, India R Kumar Department of Mathematics, Kurukshetra University, Kurukshetra, Haryana, India N Sharma Department of Mathematics, MM(DU), Mullana, Ambala, India Journal Article 2025 11 24 In this paper, a unified model of fractional order photothermoelastic based on hyperbolic two temperature (HTT) is developed. Fractional order derivatives, namely Riemann-Liouville (RL),Caputo-Fabrizio(CF),Atangana-Baleanu (AB) and Tempered-Caputo(TC) are used to propose this model. Two dimensional axisymmetric problem is explored in the assumed model by employing Laplace and Henkel transforms. Integral transform technique reduces the system of equations into ordinary differential equation. The arbitrary constants in the solution are determined by considering the loading environment on the surface. Three different categories of the sources are taken to explore the application of the problem as (i) normal force (ramp type) (ii) distributed thermal source (iii) concentrated carrier density source. In the new domain, the closed form expressions of physical quantities like displacement, normal stress, conductive temperature field and carrier density distribution are derived. The numerical inversion method is employed to recover the results in a physical domain. The solutions are presented graphically to know the impact of various fractional order derivatives in case of hyperbolic two- temperature(HTT), two-temperature(2T) and one-temperature (1T) for different fractional derivatives(RL,CF,AB and TC) on physical field quantities w.r.t. radial distance. Unique cases are also explored. The results provide are helpful for understanding the photothermoelastic interactions due to various sources and open up wide applications of using new fractional derivatives.