The study of generalized Hurwitz–Lerch zeta function and fractional kinetic equations

References

• Chaudhry, M. A., Qadir, A., Rafique, M., & Zubair, S. M. (1997). Extension of Euler’s beta function. Journal of Computational and Applied Mathematics, 78(1), 19–32. https://doi.org/10.1016/S0377-0427(96)00102-1
   Web of Science ®Google Scholar
• Chaudhry, M. A., Qadir, A., Srivastava, H. M., & Paris, R. B. (2004). Extended hypergeometric and confluent hypergeometric functions. Applied Mathematics and Computation, 159(2), 589–602. https://doi.org/10.1016/j.amc.2003.09.017
   Web of Science ®Google Scholar
• Choi, J., Rathie, A. K., & Parmar, R. K. (2014). Extension of extended beta, hypergeometric and confluent hypergeometric functions. Honam Mathematical Journal, 36(2), 357–385. https://doi.org/10.5831/HMJ.2014.36.2.357
   Google Scholar
• Erdélyi, A. (1953). Higher transcendental functions (Vols. vol-1). MacGraw-Hill.
   Google Scholar
• Garg, M., Jain, K., & Kalla, S. L. (2008). A further study of general Hurwitz–Lerch zeta function. Algebras Groups Geom, 25, 311–319.
   Google Scholar
• Gelfand, I. M., & Shilov, G. E. (1964). Generalized function, application of harmonic analysis (Vol. 4). Academic Press.
   Google Scholar
• Goyal, S. P., & Laddha, R. K. (1997). On the generalized Riemann zeta functions and the generalized Lambert transform. Ganita Sandesh, 11(2), 99–108.
   Google Scholar
• Haubold, H. J., & Mathai, A. M. (2000). The fractional kinetic equation and thermonuclear functions. Astrophysics and Space Science, 327(1/4), 53–63. https://doi.org/10.1023/A:1002695807970
   Google Scholar
• Hohenberg, P. C., & Halperin, B. I. (1977). Theory of dynamic critical phenomena. Reviews of Modern Physics, 49(3), 435–479. https://doi.org/10.1103/RevModPhys.49.435
   Web of Science ®Google Scholar
• Khan, N. U., & Husain, S. (2022). A note on extended beta function involving generalized Mittag-Leffler function and its applications. TWMS Journal of Applied and Engineering Mathematics, 12(1), 71.
   Web of Science ®Google Scholar
• Khan, N. U., Husain, S., & Khan, M. I. (2023). Analysis of an extended Whittaker function and its properties. Honam Mathematical Journal, 45(2), 184–197.
   Web of Science ®Google Scholar
• Khan, N. U., Husain, S., & Khan, O. (2023). A novel kind of new Beta logarithmic function and their properties. Hacettepe Journal of Mathematics and Statistics, 52(4), 945–955. https://doi.org/10.15672/hujms.1153572
   Web of Science ®Google Scholar
• Khan, N. U., Husain, S., Usman, T., & Araci, S. (2022). Results concerning the analysis of multi-index Whittaker function. Journal of Mathematics, 2022, 1–10. https://doi.org/10.1155/2022/3828104
   Web of Science ®Google Scholar
• Kourganoff, V. (1973). Introduction to the physics of stellar interiors (Vol. 34). D. Reidel Publishing Co.(Astrophysics and Space Science Library).
   Google Scholar
• Lin, S. D., & Srivastava, H. M. (2004). Some families of the Hurwitz–Lerch zeta functions and associated fractional derivative and other integral representations. Applied Mathematics and Computation, 154(3), 725–733. https://doi.org/10.1016/S0096-3003(03)00746-X
   Web of Science ®Google Scholar
• Mainardi, F. J. (1994). Alloys Compd. Chaos, Solitons & Fractals, 211/212, 534. https://doi.org/10.1016/0925-8388(94)90560-6
   Google Scholar
• Nadeem, R., Usman, T., Nisar, K. S., & Baleanu, D. (2020). Analytical properties of the Hurwitz–Lerch zeta function. Advances in Difference Equations, 2020(1), 1–15. https://doi.org/10.1186/s13662-020-02924-2
   PubMed Web of Science ®Google Scholar
• Novikov, E. A. (1994). On Markov modelling of turbulence. Journal of Fluid Mechanics, 280, 69–93. https://doi.org/10.1017/S0022112094002855
   Web of Science ®Google Scholar
• Parmar, R. K., & Raina, R. K. (2014). On a certain extension of the Hurwitz–Lerch zeta function. Annals of West University of Timisoara-Mathematics and Computer Science, 52(2), 157–170. https://doi.org/10.2478/awutm-2014-0017
   Google Scholar
• Raina, R. K., & Chhajed, P. K. (2004). Certain results involving a class of functions associated with the Hurwitz zeta function. Acta Mathematica Universitatis Comenianae, New Series, 73(1), 89–100.
   Google Scholar
• Srivastava, H. M., & Choi, J. (2001). Series associated with the zeta and related functions (Vol. 530). Springer Science and Business Media.
   Google Scholar
• Srivastava, H. M., & Choi, J. (2011). Zeta and q-zeta functions and associated series and integrals. Elsevier. https://doi.org/10.1016/C2010-0-67023-4
   Google Scholar
• Wiman, A. (1905). Uber den Fundamentalsatz in der Teorie der Funktionen. Acta Mathematica, 29(1), 191–201. https://doi.org/10.1007/BF02403202
   Google Scholar