Research Interests

  • Variable Exponent Lebesgue Spaces
  • Analysis of Partial Differential Equations (PDEs)
  • Analysis of Stochastic Differential Equations (SDEs)
  • Stochastic Analysis & Applications

Research Specialization Keywords

Variable Exponent Lebesgue-Sobolev Spaces; p(x)-Laplacian; Variational Methods; PDEs; Topological Methods; Monotone Operator Methods; Nonlinear Analysis; SDEs; Stochastic Analysis and Applications; Measure-Theoretic Probability.

Research In Progress

  • Analysis & Applications of SDEs with state-dependent variable exponent drift and diffusion
  • Analysis & Applications of PDEs in variable exponent Lebesgue spaces
  • The interplay of probability theory and PDEs
  • Probabilistic models of finance and mathematical physics

Research Funding (Awards & Grants)

  • External Funding Application: Applied for NSERC-Discovery Grants Program Nov 2025, in process. Website
  • Athabasca University Academic Research Fund-Publication Award (2025)
  • Athabasca University Research Incentive Account (Grant No: 140111RIA, 2023-2027)
  • International Postdoctoral Research Fellowship Program. Scientific and Technological Research Council of Turkey (TUBITAK) (Grant No: 1059B191400450, 2014-2015). Website
  • Dicle University Scientific Project Research Management (DUPAB) Grant (2007 - 2009)
    for the Research Project: The Solutions of Parabolic and Elliptic Equations with Standard and Nonstandard Growth Conditions in the Variable Exponent Lebesgue-Sobolev Spaces.

Refereed Book & Book Chapters

  • Nontrivial weak solutions of a quasilinear equation involving p-Laplace operator (as Author), in Advances in Mathematics and Computer Science Vol.2, 2019. ISBN 978-93-89562-00-2 (Print) ISBN 978-93-89562-01-9 (eBook). DOI: 10.9734/bpi/amacs/v2. Website
  • A Closer Look at Boundary Value Problems (as Editor), 2020. Nova Science Publishers, Inc. ISBN: 978-1-53617-857-9. Website

Refereed Conference Proceedings

  • A new solution of some weighted problems for Riemann-Liouville and Weyl operators (with S. Ograş, R. Mashiyev) (2009), Proceedings of the 6th International ISAAC Congress, Ankara, Turkey, 13 – 18 August 2007. Website

Refereed Journal Articles

Published/Accepted
  1. Solutions of a double phase singular Kirchhoff type equation with nonstandard growth (with A. Razani), FILOMAT. Accepted (2026). Website
  2. Nehari manifold approach for a singular multi-phase variable exponent problem, Quaestiones Mathematicae, 1–21. (2026). Website
  3. Monotone operator methods for a class of nonlocal multi-phase variable exponent problems. Acta Applicandae Mathematicae. Vol. 201, article number 7 (2026). Website
  4. Existence and multiplicity of solutions for a discrete fourth-order boundary value problem (with M. Boroun, S. Heidarkhani), Journal of Nonlinear Evolution Equations and Applications. Accepted (2025). Website
  5. Anisotropic singular equation with (p(⋅), q(⋅))-Laplacian operator and Hardy-type potential, Acta Universitatis Sapientiae Mathematica. Vol. 17, article number 18 (2025). Website
  6. Existence results for the Cox–Ingersoll–Ross model with variable exponent diffusion, AIMS Mathematics 10(9) (2025), 22106–22126. Website
  7. Three Solutions for a double-phase variable-exponent Kirchhoff problem, Mathematics 13(15) (2025), 2462. Website
  8. Singular p(x)-Laplacian equation with application to boundary layer theory, Applicable Analysis 104(13) (2025), 2546–2566. Website
  9. Existence results for a class of singular p(x)–Kirchhoff equations, Complex Variables and Elliptic Equations 70(7) (2025), 1222–1253. Website
  10. On a p(x)-Kirchhoff problem with variable singular and sublinear exponents, Taiwanese Journal of Mathematics 29(2) (2025), 379–402. Website
  11. On a p(x)–Kirchhoff-type equation with singular and superlinear nonlinearities, Differential Equations and Dynamical Systems, (2024). Website
  12. On an anisotropic p(·)-Laplace equation with variable singular and sublinear nonlinearities, Communications in Analysis and Mechanics 16(3) (2024), 554–577. Website
  13. Multiple solutions for a class of p(x)–Kirchhoff-type equations (with S. Heidarkhani, A. Ghobadi), Applied Mathematics E-Notes 22 (2022), 160–168. Website
  14. Solutions of Ginzburg–Landau-type equations involving variable exponent, Thai Journal of Mathematics 20(1) (2022), 369–384. Website
  15. Critical points approaches to a nonlocal elliptic problem driven by p(x)–biharmonic operator (with S. Heidarkhani, S. Moradi), Georgian Mathematical Journal 29(1) (2021), 55–69. Website
  16. A Class of nonlocal elliptic equations in Orlicz–Sobolev spaces (with B. Suer, V. Turut), Journal of Abstract and Computational Mathematics 6(2) (2021), 16–29. Website
  17. On a nonlocal problem with indefinite weights in Orlicz–Sobolev space (with N. T. Chung), Communications of the Korean Mathematical Society 35(2) (2020), 517–532. Website
  18. A variational approach to the existence of infinitely many solutions for difference equations (with M. K. Moghadam, S. Tersian), Journal of New Research in Mathematics 5(22) (2020), 99–110.
  19. A topological result for a class of anisotropic difference equations, Annals of the University of Craiova – Mathematics and Computer Science Series 46(2) (2019), 328–343. Website
  20. On some classes of nonlocal problems in Musielak–Sobolev spaces, Southeast Asian Bulletin of Mathematics 43 (2019), 791–814.
  21. Positive ground state solutions to a nonlocal singular elliptic problem, Canadian Journal of Applied Mathematics 1(1) (2019), 1–14. Website
  22. On a nonlocal problem involving a nonstandard nonhomogeneous differential operator (with B. Suer), Journal of Elliptic and Parabolic Equations 5(1) (2019), 47–67. Website
  23. On a Robin problem in Orlicz–Sobolev spaces (with K. Suslu), TWMS Journal of Applied and Engineering Mathematics 9(2) (2019), 246–256. Website
  24. Solutions to p(x)–Laplace type equations via nonvariational techniques, Opuscula Mathematica 38(3) (2018), 291–305. Website
  25. Multivalued elliptic operators with nonstandard growth (with A. Pankov), Advances in Nonlinear Analysis 7(1) (2018), 35–48. Website
  26. Existence results to a nonlinear p(k)–Laplacian difference equation (with M. K. Moghadam), Journal of Difference Equations and Applications 23(10) (2017), 1652–1669. Website
  27. On a nonlocal Neumann problem in Orlicz–Sobolev spaces, Journal of Nonlinear Functional Analysis 2017 (2017), Article ID 42, 1–11. Website
  28. Existence results for anisotropic discrete boundary value problems, Electronic Journal of Differential Equations 148 (2016), 1–11. Website
  29. On a nonlocal problem involving the generalized anisotropic p(⋅)-Laplace operator, Annals of the University of Craiova – Mathematics and Computer Science Series 43(2) (2016), 259–272. Website
  30. Solutions to a system of p(x)–Kirchhoff discrete boundary value problems, Nonlinear Studies 23(4) (2016), 665–674. Website
  31. Existence of solutions for nonlocal problems in Sobolev–Orlicz spaces via Monotone method (with R. Mashiyev, N. T. Chung), Electronic Journal of Mathematical Analysis and Applications 4(1) (2016), 63–73. Website
  32. Positive periodic solutions of nonlinear differential equations system with nonstandard growth (with R. Ayazoglu), Applied Mathematics Letters 43 (2015), 5–9. Website
  33. Nontrivial solutions of discrete nonlinear equations with variable exponent (with A. Pankov), Journal of Mathematical Analysis and Applications 431 (2015), 22–33. Website
  34. Nontrivial weak solutions of a quasilinear equation involving p-Laplace operator, British Journal of Mathematics & Computer Science 6(2) (2015), 112–118. Website
  35. Existence of solutions for fourth-order elliptic equations of Kirchhoff type (with F. Wang, Y. An), Journal of Mathematical Analysis and Applications 409(1) (2014), 140–146. Website
  36. Existence of three solutions for a quasilinear elliptic equation involving the p(x)–Laplacian (with R. Mashiyev), Sarajevo Journal of Mathematics 10(23) (2014), 1–13. Website
  37. Existence and uniqueness of solutions of a nonlocal problem involving the p(x)–Laplacian (with R. Mashiyev), Annals of the University of Craiova – Mathematics and Computer Science Series 41(1) (2014), 30–37. Website
  38. Existence results for a nonlocal problem involving the p-Laplacian, Universal Journal of Applied Mathematics 2(3) (2014), 153–159. Website
  39. Ni–Serrin type equations arising from capillarity phenomena with non-standard growth, Boundary Value Problems (2013), Article 55, 1–18. Website
  40. Existence and multiplicity of solutions for Dirichlet problems involving the p(x)–Laplacian, Electronic Journal of Differential Equations 14 (2013), 1–9. Website
  41. Existence of solutions for an elliptic equation with nonstandard growth (with R. Mashiyev, B. Cekic), International Journal of Pure and Applied Mathematics 86(1) (2013), 131–139. Website
  42. Solutions of a nonlocal elliptic problem involving p(x)–Kirchhoff-type equation, Applied Mathematics 3(2) (2013), 56–60. Website
  43. Existence and uniqueness of solutions for a quasilinear elliptic equation involving p-Laplacian (with R. Mashiyev), International Journal of Differential Equations and Applications 12(2) (2013), 95–102. Website
  44. Existence results for a nonlocal problem involving the p(x)-Laplacian, Pure and Applied Mathematics Journal 2(1) (2013), 20–27. Website
  45. Solutions of nonlocal (p₁(x), p₂(x))-Laplacian equations (with R. Mashiyev), International Journal of Partial Differential Equations, Vol. 2013, Article ID 364251, 7 pages. Website
  46. Existence of weak solutions for a nonlocal problem involving the p(x)–Laplace operator, Universal Journal of Applied Mathematics 1(3) (2013), 192–197. Website
  47. Solutions of an anisotropic nonlocal problem involving variable exponent (with R. Mashiyev, B. Cekic), Advances in Nonlinear Analysis 2(3) (2013), 325–338. Website
  48. On an elliptic system of p(x)–Kirchhoff-type under Neumann boundary condition (with Z. Yucedag, R. Mashiyev), Mathematical Modelling and Analysis 17(2) (2012), 161–170. Website
  49. L^p(x)(\Omega)-estimates of vector fields and applications to magnetostatics problems (with B. Cekic, A. V. Kalinin, R. Mashiyev), Journal of Mathematical Analysis and Applications 389(2) (2012), 838–851. Website
  50. Existence and multiplicity of weak solutions for nonuniformly elliptic equations with nonstandard growth (with R. Mashiyev, B. Cekic, Z. Yucedag), Complex Variables and Elliptic Equations 57(5) (2012), 579–595. Website
  51. Existence and multiplicity of solutions of the p(x)-Kirchhoff type equation via genus theory (with B. Cekic, R. Mashiyev), Mathematical Methods in the Applied Sciences 34(14) (2011), 1751–1759. Website
  52. The Nehari manifold approach for a Dirichlet problem involving the p(x)–Laplacian (with R. Mashiyev, S. Ogras, Z. Yucedag), Journal of the Korean Mathematical Society 47(4) (2010), 845–860. Website
  53. Existence of solutions for a class of elliptic systems in ℝN involving the (p(x), q(x))-Laplacian (with S. Ogras, R. Mashiyev, Z. Yucedag), Journal of Inequalities and Applications, Article 612938 (2008). Website
Submitted
  1. On the existence, uniqueness and stability of solutions of SDEs with state-dependent variable exponent. Under review.
  2. Positive weak solutions of a double-phase variable exponent problem with a fractional-Hardy-type singular potential and superlinear nonlinearity. Under review.
  3. Stochastic representation of solutions for the parabolic Cauchy problem with variable exponent coefficients. Under review.
  4. On the geometric Brownian motion with state-dependent variable exponent diffusion term. Under review.
  5. Existence and uniqueness results for a singular elliptic problem governed by an anisotropic (p(⋅), q(⋅))-Kirchhoff-type operator. Under review.
  6. Variational and nonvariational solutions for double phase variable exponent problems. Under review.
  7. Anisotropic Variable exponent Kirchhoff-type equation with double singularity (with B. Cekic, Z. Yucedag). Under review.
  8. Singular Kirchhoff–Ginzburg–Landau-type equation with variable Exponent (with B. Cekic, Z. Yucedag). Under review.
  9. On a p(x)-Kirchhoff Equation with double singularity exponent (with B. Cekic, Z. Yucedag). Under review.
Work in progress
  1. On a singular double phase variable exponent problem: A topological approach

Presentations (Invited Talks & Contributed Talks & Workshops)

List
  1. Existence of solutions for a singular double phase variable exponent problem with (p(.),q(.))- Hardy-type potential, the Canadian Mathematical Society 80th Anniversary Winter Meeting, December 5-8, 2025, Toronto, Ontario.
  2. A viscosity solution approach to the Feynman-Kac formula for a one-dimensional parabolic PDE with variable exponent coefficient, the Canadian Mathematical Society 80th Anniversary Winter Meeting, December 5-8, 2025, Toronto, Ontario.
  3. Online Mathematics Assessment: The Innovative Methods and Challenges of Integrity, the Canadian Mathematical Society MathEd Meeting (Online), November 28-29, 2025.
  4. Recent Trends in Stochastic Partial Differential Equations, Workshop, November 17-21, 2025, Simons Laufer Mathematical Sciences Institute (SLMath), University of California, Berkeley.
  5. SDEs with state-dependent variable exponent drift and diffusion terms, Analysis Seminar, Oct 29, 2025, Department of Mathematics, University of Alabama, Tuscaloosa.
  6. A generalized stochastic volatility model, Alberta Mathematics Dialogue, May 1-2, 2025, University of Calgary, Calgary.
  7. Enhancing mathematical learning with interactive content and adaptive online assessments (with A. Beltaos, J. Greenwood-Lee), Alberta Mathematics Dialogue, May 1-2, 2025, University of Calgary, Calgary.
  8. The regularization method for multivalued elliptic PDEs with variable exponent, International Conference on Applied Mathematics, 29–31 October 2020, University of Craiova, Craiova, Romania.
  9. Variational approach for analysis of PDEs, Mathematics Colloquium, Grande Prairie Regional College, Science Department, February 2020, Grande Prairie.
  10. Existence and uniqueness results for a Dirichlet problem in Orlicz–Sobolev spaces, International Conference on Mathematics and Mathematics Education (ICMME-2017), 11–13 May 2017, Şanlıurfa, Turkey.
  11. Nontrivial solutions for a Dirichlet problem in Orlicz–Sobolev spaces, ICMME-2017, 11–13 May 2017, Şanlıurfa, Turkey.
  12. Solutions of an anisotropic Kirchhoff problem involving variable exponent, ICMME-2017, 11–13 May 2017, Şanlıurfa, Turkey.
  13. Solutions of Kirchhoff problem in anisotropic variable exponent spaces, ICMME-2017, 11–13 May 2017, Şanlıurfa, Turkey.
  14. On some elliptic problems in Orlicz–Sobolev spaces, International Health and Natural Sciences Conference (INHSC 2017), 19–21 October 2017, Antalya, Turkey.
  15. Solutions to a nonlocal elliptic problem in Orlicz–Sobolev spaces, INHSC 2017, 19–21 October 2017, Antalya, Turkey.
  16. Solutions of generalized anisotropic problems in variable exponent spaces, INHSC 2017, 19–21 October 2017, Antalya, Turkey.
  17. A system of anisotropic discrete boundary value problems, International Engineering, Science and Education Conference, 1–3 December 2016, Diyarbakır, Turkey.
  18. Existence of three solutions to a nonlinear difference equation involving p(k)-Laplace operator, International Engineering, Science and Education Conference, 1–3 December 2016, Diyarbakır, Turkey.
  19. Variable Lebesgue spaces and variational approach, Morgan State University, Department of Mathematics, Mathematics Colloquium, November 2014, Baltimore, U.S.A.
  20. Existence and uniqueness of an elliptic equation with p(x)-Laplace operator, XXVI. National Mathematics Symposium, 4–7 Sept, 2013, Dicle University, Diyarbakır, Turkey.
  21. Power-type weighted Hardy and Hankel operators in variable exponent Morrey space, “Operators in General Morrey-Type Spaces and Applications” (Dedicated to the 70th Birthday of Prof. Victor I. Burenkov), Ahi Evran University, Kırşehir, Turkey, 20–27 May 2011.
  22. Maximal and Riesz operators in weighted variable exponent Morrey space, same event, Ahi Evran University, Kırşehir, Turkey, 20–27 May 2011.
  23. Existence of solutions for nonuniformly elliptic equations of p(x)-Laplacian type, 3rd International Conference on Differential Equations and Applications, Lviv, Ukraine, 3–6 November 2010.
  24. Existence of solutions for a p(x)-Laplacian in ℝ(N), Workshop on Differential Equations and Applications, Pamukkale University, Denizli, Turkey, 18–20 April 2008.
  25. A new solution of some weighted problems for the Riemann–Liouville and Weyl operators, 6th International ISAAC Congress, 13–18 August 2007, Middle East Technical University (METU), Ankara, Turkey.