I am a Professor at Fergana State University and a leading researcher of the V.I.Romanovskiy Institute of Mathematics, Uzbekistan Academy of Sciences. I am also a long-term visitor and collaborator of Michael Ruzhansky and UGent Analysis & PDE group.

In 2006 I have got a Ph.D. degree and in 2010 I had a postdoc position at the University of Santiago de Compostela, Spain. The second postdoc position I had in 2016 at the Sultan Qaboos University, Oman.

I am a member of international mathematical society ISAAC, Young affiliate of the TWAS (The World Academy of Sciences).

I am a reviewer of several international journals such Applied Mathematics Letters, Results in Mathematics and etc.

Member of editorial board of the Uzbek Mathematical Journal (http://uzmj.mathinst.uz), vice-editor of an electronic journal “Bulletin of the Institute of Mathematics”(http://mib.mathinst.uz).

My research interests are

– Direct and inverse problems for integer and fractional order Partial differential equations;

– Special functions, including different Mittag-Leffler type functions and their applications in Fractional PDE.

Publications:

- Karimov E.T., Toshtemirov B.H. On a time-nonlocal boundary value problem for time-fractional partial differential equation. doi:10.13140/RG.2.2.21024.05129
- A boundary-value problem for a mixed type equation involving hyper-Bessel fractional differential operator and Hilfer’s bi-ordinal fractional derivative. arxiv:submit/3840114 [math.AP] 15 Jul 2021
- N.Al-Salti, E.T.Karimov. Inverse source problems for degenerate time-fractional PDE. Submitted to
*Progr.Fract.Differ.Appl*. in 02/05/2019. - E.T.Karimov, B.H.Toshtemirov. Tricomi type problem with integral conjugation condition for a mixed type equation with the hyper-bessel fractional differential operator.
*Bulletin**of the Institute of Mathematics*, No 4, 9-14 (2019) - E.T.Karimov, S.Kerbal. Tricomi type problem for mixed type equation with sub-diffusion and wave equation.
*FDU. Ilmiy khabarlar*, No 3, 9-14 (2019) - E.T.Karimov. Tricomi type boundary value problem with integral conjugation condition for a mixed type equation with Hilfer fractional operator.
*Bulletin of the Institute of Mathematics*, No 1, 19-26 (2019) - Fatma Al-Musalhi, Nasser Al-Salti, Erkinjon Karimov. Initial and boundary value problems for fractional differential equations involving Atangana-Baleanu derivative.
*SQU Journal**for Science*, 23(2), 137-146 (2018) - Fatma Al-Musalhi, Nasser Al-Salti, Erkinjon Karimov. Initial boundary value problems for a fractional differential equation with hyper-Bessel operator.
*Fract. Calc. Appl. Anal.*21(1), 200-219 (2018) - Karimov E.T. and Sadarangani K. Existence of a unique positive solution for a singular fractional boundary value problem.
*Carpathian J. Math*. 34(1), 57-64 (2018) - Erkinjon Karimov, Sardor Pirnafasov. Higher order multi-term time-fractional partial differential equations involving Caputo-Fabrizio derivative.
*Electronic Journal of**Differential Equations*, No 243, 1-11 (**2017**) - E.T.Karimov, S.Kerbal, N.Al-Salti
**.**Inverse source problem for multi-term fractional mixed type equation. M.Ruzhansky et al. (eds.), Advances in Real and Complex Analysis with Applications,*Trends in Mathematics*, 289-301 (**2017**). - E.Karimov, N.Al-Salti, S.Kerbal. An inverse source non-local problem for a mixed type equation with a Caputo fractional differential operator. East Asian Journal of Applied Mathematics. 7(2), 417-438 (2017).
- E.T.Karimov, A.S.Berdyshev and N.A.Rakhmatullaeva. Unique solvability of a non-local problem for mixed-type equation with fractional derivative. Mathematical Methods in the Applied Sciences. 40(8), 2994-2999 (2017)
- Agarwal P., Karimov E., Mamchuev M., Ruzhansky M., On boundary-value problems for a partial differential equation with Caputo and Bessel operators, in Novel Methods in Harmonic Analysis, Vol. 2, pp. 707-719, (Pesenson, I., Le Gia, et al. editors), Applied and Numerical Harmonic Analysis. Birkhauser Basel, 2017.
- S.Kerbal, E.Karimov, N.Rakhmatullaeva. Non-local boundary problem with integral form transmitting condition for fractional mixed type equation in a composite domain. Mat. Model. Nat. Phenom. 12(3), 95-104 (2017)
- P.Agarwal, A.Berdyshev and E.Karimov. Solvability of a non-local problem with integral transmitting condition for mixed type equation with Caputo fractional derivative. Results in Mathematics. 71(3), 1235-1257 (2017)
- N.Al-Salti, E.T.Karimov and S.Kerbal. Boundary-value problems for fractional heat equation involving Caputo-Fabrizio derivative. New Trends in Mathematical Sciences.Vol.4, No 4, 79-89 (2016).
- E.T.Karimov, B.Lopez and K.Sadarangani. About the existence of solutions for a hybrid nonlinear generalized fractional pantograph equation. Fractional Differential Calculus.

Vol.6, No 1, 95-110 (2016). - N.Al-Salti, E.T.Karimov and K.Sadarangani. On a differential equation with Caputo-Fabrizio fractional derivative of order 12 and application to mass-spring-damper system. Progr.Fract.Differ.Appl. 2, No 4, 257-263 (2016).
- M.S. Salakhitdinov, E.T.Karimov. Uniqueness of inverse source non-local problem for fractional order mixed type equation. Euroasian Mathematical Journal, No 1, 74-83 (2016).
- P.Agarwal, S.V.Rogosin, E.T.Karimov and M.Chand. Generalized fractional integral operators and the multivariable H-function. Journal of Inequalities and Applications.(2015) 2015:350. DOI 10.1186/s13660-015-0878-y.

- Pengbin Feng, E.T.Karimov. Inverse source problems for time-fractional mixed parabolic-hyperbolic type equations. Journal of Inverse and Ill-posed problems. Vol.23, No 4, 2015, pp.339-353.
- P.Agarwal, M.Chand, E.T.Karimov. Certain image formulas of generalized hypergeo- metric functions. Applied Mathematics and Computation. 266(2015), pp.763-772.
- M.S.Salakhitdinov, E.T.Karimov. On a nonlocal problem with gluing condition of integral form for parabolic-hyperbolic equation with Caputo operator. Reports of the Academy of Sciences of the Republic of Uzbekistan (DAN RUz), No 4, 2014, pp.6-9.
- Abdumauvlen S. Berdyshev, Erkinjon T. Karimov and Nazgul S. Akhtaeva. On a boundary- value problem for the parabolic-hyperbolic equation with the fractional derivative and the sewing condition of the integral form. AIP Proceedings, Vol.1611, 2014, pp.133-137.
- E.T.Karimov. Boundary value problems with integral conjugation conditions for parabolic- hyperbolic equation with the Caputo operator in a domain with deviation from the characteristics. Uzbek Mathematical Journal (UzMJ), 2014, No 2, pp.66-77.
- E.T.Karimov, N.A.Rakhmatullaeva. On a nonlocal problem for mixed parabolic-hyperbolic type equation with nonsmooth line of type changing. Asian-European Journal of Mathematics (AEJM). Vol.7, No 2 (2014) 1450030 (9 pages).
- E.T.Karimov, J.S.Akhatov. A boundary problem with integral gluing condition for a parabolic-hyperbolic equation involving the Caputo fractional derivative. Electronic Journal of Differential Equations (EJDE), Vol. 2014 (2014), No. 14, pp. 1-6.
- A.S.Berdyshev, A.Cabada, E.T.Karimov and N.S.Akhtaeva. On the Volterra property of a boundary problem with integral gluing condition for a mixed parabolic-hyperbolic equation. Boundary Value Problems (BVP), (2013) 2013:94.
- J.M.Rassias, E.T.Karimov. Boundary-value problems with non-local condition for degenerate parabolic equations. Contemprorary Analysis and Applied Mathematics (CAAM), Vol. 1, No 1 (2013), pp. 42-48.
- M.S.Salakhitdinov, E.T.Karimov. Spatial boundary problem with the Dirichlet-Neumann condition for a singular elliptic equation. Applied Mathematics and Computation (AMC), 219 (2012), pp.3469-3476.
- Nieto J.J. and Karimov E.T. On an analogue of the Holmgren’s problem for 3d singular elliptic equation. Asian and European Journal of Mathematics (AEJM), Vol.5, No 2 (2012) 1250021 (18 pages) DOI: 10.1142/S1793557112500210.
- A.S. Berdyshev, A.Cabada, E.T.Karimov. On a non-local boundary problem for a parabolic-hyperbolic equation involving Riemann-Liouville fractional differential operator. Nonlinear Analysis 75(2012), 3268-3273.
- A.S.B erdyshev, E.T.Karimov and N.Akhtaeva. Boundary value problems with integral gluing conditions for fractional order mixed type equation. International Journal of Differential Equations (IJDE), Volume 2011, Article ID 268465, 10 pages doi:10.1155/2011/268465.
- Nieto J.J. and Karimov E.T. The Dirichlet problem for 3-D elliptic equation with two singular coefficients. Computers and Mathematics with applications (CAMWA), 62(1), 2011, pp.214-224.
- Urinov A.K. and Karimov E.T. On fundamental solutions for 3D singular elliptic equations with a parameter, Applied Mathematics Letters (AML), 24(3), 2011, pp.314-319.
- Rassias J.M. and Karimov E.T. Boundary-value problems with initial non-local condition for parabolic equations with parameter. European Journal of Pure and Applied Mathematics (EJPAM), 3(6), 2010, pp.948-957.
- Karimov E.T. A boundary-value problem for three-dimensional elliptic equation with singular coefficients. Uzbek Mathematical Journal, Number 2, 2010, pp. 56-66.
- Karimov E.T. On the Dirichlet problem for three dimensional elliptic equation with singular coefficient. Reports of the Academy of Sciences of the Republic of Uzbekistan (DAN RUz), Number 2, 2010, pp. 9-12.
- Karimov E.T. On a boundary problem with Neumann’s condition for 3D singular elliptic equations, Applied Mathematics Letters (AML), 23(5), 2010, pp.517-522.