q-Exponential fixed point theorem for mixed monotone operator with q-fractional problem

Document Type : Research Paper

Authors

University of Mazandaran, Babolsar, Iran.

Abstract

In this work, we examine the existence and uniqueness(EU) of q-Exponential positive solution (q-EPS) of the hybrid q-fractional boundary value problem (q-FBVP).
We prove the q-Exponential fixed point theorem (q-EFPT) with a new set $\rho_{h,e_{1}}$ in the Banach space E to check the EU of q-EPS of the q-FBVP. In the long run, an exemplum is given to show the correctness of our results. 

Keywords

Main Subjects


  • [1]  A. Boutiara and M. Benbachir, Existence and uniqueness results to a fractional q-difference coupled system with integral boundary conditions via topological degree theory, Int. J. Nonlinear Anal. Appl,13(1) (2022), 3197-3211.
  • [2]  T. Ernst, A comprehensive treatment of q-calculus, Springer Basel Heidelberg New york Dordrecht London, (2012).
  • [3]  M. Gholami and A. Neamaty, λ-fixed point theorem with kinds of functions of mixed monotone operator, Journal of Applied Analysis and Computation, 13(4), (2023).
  • [4]  A. A. Kilbas, H. M. Srivastava, and J. J. Trujillo, Theory and applications of fractional differential equations, Elsevier, Elsevier B. v. Amsterdam, (2006).
  • [5]  Y. Liu, C. Yan, and W. Jiang, Existence of the unique nontrivial solution for mixed fractional differential equations, Journal of Function Spaces.
  • [6]  I. Podlubny, Fractional differential equations, Mathematics in Science and Engineering, Academic Press, New York. (1999).
  • [7]  P. M. Rajkovic, S. D. Marinkovic, and M. S. Stankovic, Fractional integrals and derivatives in q-calculus, Applicable Analysis and Discrete Mathematics, (2007), 311–323.
  • [8]  Y. Sang, L. U. He, Y. L. Wang, Y. Ren, and N. Shi, Existence of positive solutions for a class of fractional differential equations with the derivative term via a new fixed point theorem, Advances in Difference Equations.
  • [9]  Y. Sang and Y. Ren, Nonlinear sum operator equations and applications to elastic beam equation and fractional differential equation, Boundary Value Problems.
  • [10]  J. J. Tan and C. Cheng, Fractional boundary value problems with Riemann-Liouville fractional derivatives, Advances in Difference Equations.
  • [11]  C. Zhai, Fixed point theorems for a class of mixed monotone operators with convexity, Fixed Point Theory and Applications.
  • [12]  C. Zhai and L. Wang, ϕ-(h,e)-concave operators and applications, Journal of Mathematical Analysis and Applications, 4 (2017), 571–584.