TY - JOUR
T1 - Fixed Point Theorems in Controlled Rectangular Modular Metric Spaces with Solution of Fractional Differential Equations
AU - Ishtiaq, Umar
AU - Saleem, Naeem
AU - Farhan, Muhammad
AU - Aphane, Maggie
AU - Chowdhury, Mohammad S.R.
N1 - Publisher Copyright:
© 2025 The Author(s).
PY - 2025/1
Y1 - 2025/1
N2 - In this paper, we establish the notion of controlled rectangular modular metric space as a generalization of modular b−metric space and rectangular b−metric space. We used contraction mappings to find the existence and uniqueness of a fixed point in the framework of controlled rectangular modular metric space. We give several non-trivial examples and show the validity of contraction mappings via graphs. At the end, we utilize our main result to solve a non-linear fractional differential equation.
AB - In this paper, we establish the notion of controlled rectangular modular metric space as a generalization of modular b−metric space and rectangular b−metric space. We used contraction mappings to find the existence and uniqueness of a fixed point in the framework of controlled rectangular modular metric space. We give several non-trivial examples and show the validity of contraction mappings via graphs. At the end, we utilize our main result to solve a non-linear fractional differential equation.
KW - Controlled metric space
KW - fixed point; existence and uniqueness
KW - modular metric space
KW - non-linear fractional differential equations
UR - https://www.scopus.com/pages/publications/85217652414
U2 - 10.29020/nybg.ejpam.v18i1.5794
DO - 10.29020/nybg.ejpam.v18i1.5794
M3 - Article
AN - SCOPUS:85217652414
SN - 1307-5543
VL - 18
JO - European Journal of Pure and Applied Mathematics
JF - European Journal of Pure and Applied Mathematics
IS - 1
M1 - 5794
ER -