I am a Leading Researcher at V.I.Romanovskiy Institute of Mathematics, Uzbekistan Academy of Sciences and Postdoctoral Fellow at Analysis & PDE group, Ghent University, Belgium.

In 2006 I have got a PhD and in 2010 obtained DSc (Doctor of Sciences in Mathematics and Physics). I had my first 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 Uzbek Mathematicsl Society, International mathematical society ISAAC, Young affiliate of the TWAS (The World Academy of Sciences).

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

My research interests are

Publications:

2024: (5 papers)

1. E.Karimov, N.Tokmagambetov and D.Usmonov. (2024) Inverse-initial problem for time-degenerate PDE involving the bi-ordinal Hilfer derivative. Cybernetics and Systems Analysis, 2024, Vol. 60, No 5, pp. 799-809.
2. E.T.Karimov and N.E.Tokmagambetov. (2024) Inverse Problem on Finding Unknown Time-Moment for Mixed Wave-Diffusion Equation. Lobachevskii Journal of Mathematics, 2024, Vol.45, No 7, pp.3323-3331.
3. E. Karimov, Z. Sobirov, and J. Khujakulov. (2024) A non-local problem for a time-fractional differential equation with the Hilfer operator on metric graph, Math. Meth. Appl. Sci. (2024), 1–19, DOI 10.1002/mma.10207
4. Karimov E., Tokmagambetov N., Khasanov Sh. (2024) Inverse Problems for Time-Fractional Mixed Equation Involving the Caputo Fractional Derivative. In: Ruzhansky, M., Van Bockstal, K. (eds) Extended Abstracts 2021/2022. APDEGS 2021. Trends in Mathematics, vol 2. Birkhäuser, Cham. https://doi.org/10.1007/978-3-031-42539-4_20
5. Karimov, E., Tokmagambetov, N., Toshpulatov, M. (2024). On a Mixed Equation Involving Prabhakar Fractional Order Integral-Differential Operators. In: Ruzhansky, M., Van Bockstal, K. (eds) Extended Abstracts 2021/2022. APDEGS 2021. Trends in Mathematics, vol 2. Birkhäuser, Cham. https://doi.org/10.1007/978-3-031-42539-4_25

2023: (3 papers)

1. Al-Salti, N., Karimov, E. & Kerbal, S. A boundary problem for the time-fractional Hallaire–Luikov moisture transfer equation with Hilfer derivative. Comp. Appl. Math. 42, 94 (2023). https://doi.org/10.1007/s40314-023-02231-y
2. Karimov E. T., Ruzhansky M., Toshtemirov B. H. Solvability of the boundary-value problem for a mixed equation involving hyper-Bessel fractional differential operator and bi-ordinal Hilfer fractional derivative. Math. Meth. Appl. Sci., 2023, Vol.46, No 1, pp.54-70.
3. Anvar Hasanov and Erkinjon Karimov. On a boundary-value problem in a bounded domain for a time-fractional diffusion equation with the Prabhakar fractional derivative. Bulletin of the Karaganda university Mathematics series. 2023, Vol.111, No 3, pp.39-46.

(2022: 6 papers)

1. E.Karimov, B.Toshtemirov. On a time-nonlocal boundary value problem for time-fractional partial differential equation. International Journal of Applied Mathematics, Vol. 35, No 3, pp.423-438 (2022)
2. Erkinjon Karimov, Michael Ruzhansky and Niyaz Tokmagambetov. Cauchy type problems for fractional differential equations, Integral Transforms and Special Functions,  Vol.33, No 1, pp.47-64 (2022)
3. N.Al-Salti, E.T.Karimov. Inverse source problems for degenerate time-fractional PDE. Progr.Fract.Differ.Appl.,  Vol.8, No 1, pp.39-52 (2022)
4. A. K. Urinov, E. T. Karimov, S. Kerbal. Boundary-value problem with an integral conjugation condition for a partial differential equation with the fractional Riemann–Liouville derivative that describes gas flows in a channel surrounded by a porous medium. Itogi nauki I tekhniki. Ser.Sovrem.mat. i ee.pril.tem.obz., 2022,  210, pp.66-76.
5. T.K.Yuldashev, E.T.Karimov. On one loaded mixed-type integro-differential equation with fractional Gerasimov-Caputo operators. Itogi nauki I tekhniki. Ser.Sovrem.mat. i ee.pril.tem.obz., 2022,  211, pp.96-113.
6. Karimov E.T., Turdiev Kh. N. Direct and inverse source problems for sub-diffusion equation involving generalized Hilfer derivative with a non-classical boundary condition. Bull. Inst. Math., 2022, Vol.5, No 5, pp.53-59.

(2021: 4 papers)

1. T. K. Yuldashev, E. T. Karimov. Mixed type integro-differential equation with fractional order Сaputo operators and spectral parameters. Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta, 2021, vol. 57, pp. 190-205.
2. Karimov E. T., Sobirov Z. A., Khujakulov J. R. Solvability of a problem for a time fractional differential equation with the Hilfer operator on metric graphs. Bull. Inst. Math., 2021, Vol.4, №4, pp. 9-18.
3. E.T.Karimov, B.H.Toshtemirov. Non-local boundary value problem for a mixed-type equation involving the bi-ordinal Hilfer fractional differential operators. Uzbek Mathematical Journal, 2021, Vol.65, Issue 2, pp.61-77.
4. Fatma Al-Musalhi and Erkinjon Karimov. On self-similar solutions of time and space fractional sub-diffusion equations. An International Journal of Optimization and Control: Theories & Applications (IJOCTA), Vol.11, No 3, pp.16-27.

 (2020: 5 papers)

1. Tursun K. Yuldashev and Erkinjon T. Karimov. Inverse Problem for a Mixed Type Integro-Differential Equation with Fractional Order Caputo Operators and Spectral Parameters. Axioms 2020, 9, 121; doi:10.3390/axioms9040121
2. E.T.Karimov. Frankl-type problem for a mixed type equation with the Caputo fractional derivative. Lobachevskii Journal of Mathematics, 2020, No 9, pp.1829-1836.
3. E.Karimov, M.Mamchuev, M.Ruzhansky. Non-local initial problem for second order time-fractional and space-singular equation. Hokkaido Mathematical Journal, 2020, Vol. 49, pp.349-361.
4. Abdumauvlen Berdyshev, Alberto Cabada and Erkinjon Karimov. On the existence of eigenvalues of a boundary value problem with transmitting condition of the integral form for a parabolic-hyperbolic equation. Mathematics, 2020, No 8, 1030: 13 pages; doi:10.3390/math8061030
5. Allen I.K., Duggal D., Nasir S., Karimov E.T. On a boundary value problem for a time-fractional wave equation with the Riemann-Liouville and Atangana-Baleanu derivatives. Bull. Inst.Math., 2020, No 1, pp.1-9.

(2019: 3 papers)

1. 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)
2. E.T.Karimov, S.Kerbal. Tricomi type problem for mixed type equation with sub-diffusion and wave equation. FDU. Ilmiy khabarlar, No 3, 10-14 (2019)
3. 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)

(2018: 3 papers)

1. 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)

2. 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)  
3. 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)

(2017: 8 papers)

1. Salakhitdinov M.S., Karimov E.T. Direct and inverse source problems for two-term time-fractional diffusion equation with Hilfer derivative. Uzbek Mathematical Journal, 4, 140-149 (2017)
2. 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)
3. 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).
4. 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).
5. 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)
6. 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.
7. 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)
8. 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)

(2016: 4 papers)

1. 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).
2. 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).
3. N.Al-Salti, E.T.Karimov and K.Sadarangani. On a differential equation with Caputo-Fabrizio fractional derivative of order  and application to mass-spring-damper system. Progr.Fract.Differ.Appl. 2, No 4, 257-263 (2016).
4. 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).

(2015: 3 papers)

1. 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.
2. 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.
3. P.Agarwal, M.Chand, E.T.Karimov. Certain image formulas of generalized hypergeo-metric functions. Applied Mathematics and Computation. 266(2015), pp.763-772.

(2014: 5 papers)

1. 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.
2. 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.
3. 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.
4. 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).
5. 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.

(2013: 2 papers)

1. 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.
2. 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.

(2012: 3 papers)

1. 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.
2. 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.
3. 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.

(2011: 3 papers)

1. A.S.Berdyshev, 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.
2. 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.
3. 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.

(2010: 4 papers)

1. 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.
2. Karimov E.T. A boundary-value problem for three-dimensional elliptic equation with singular coefficients. Uzbek Mathematical Journal, Number 2, 2010, pp. 56-66.
3. 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.
4. 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.

(2009: 1 paper)

1. Hasanov A., Karimov E.T. Fundamental solutions for a class of three-dimensional elliptic equations. Applied Mathematics Letters (AML), 22(12), 2009, pp.1828-1832.

(2008: 1 paper)

1. Karimov E.T. Some non-local problems for the parabolic-hyperbolic type equation with complex spectral parameter. Mathematische Nachrichten (MN), 281(7), 2008, pp.959-970.

(2007: 2 papers)

1. Karimov E.T., Eshmatov B.E. Boundary-value problems with continuous and special gluing conditions for parabolic-hyperbolic type equations. Central European Journal of Mathematics (CEJM), 5(4), 2007, pp.741-750.     
2. Karimov E.T. Non-local problems with special gluing condition for the parabolic-hyperbolic type equation. PanAmerican Mathematical Journal, 17(2), 2007, pp.11-20.  

(2006: 2 papers)

1. Berdyshev A.S., Karimov E.T. Non-local boundary-value problems with special gluing conditions for parabolic-hyperbolic equation. Reports of the Academy of Sciences of the Republic of Uzbekistan (DAN RUz),  Number 3, 2006,pp. 14-16.
2. Berdyshev A.S., Karimov E.T. Some-non-local problems for the parabolic-hyperbolic type equation with non-characteristic line of changing type. Central European Journal of Mathematics (CEJM), 4(2), 2006, pp.183-193.

(2005: 2 papers)

1. Karimov E.T. About the Tricomi problem for the mixed parabolic-hyperbolic type equation with spectral parameter. Complex Variables and Elliptic Equations, 50(6), 2005, pp.433-440.       
2. Berdyshev A.S., Karimov E.T. Non-local problems for parabolic-hyperbolic type equations with spectral parameter. (Russian. English, Uzbek summaries). Uzbek Mathematical Journal,Number 4, 2005,  pp.22–36.

(2003: 1 paper)

1. Karimov E.T. On the existence of a solution of two non-local problems for an equation of mixed type with a spectral parameter. (Russian. English, Uzbek summaries). Uzbek Mathematical Journal, Number 3-4, 2003,pp.16–24.