Common solution to a pair of nonlinear Fredholm and Volterra integral equations and nonlinear fractional differential equations

2021 ◽  
pp. 113907
Author(s):  
D. Ramesh Kumar
Keyword(s):  
Differential Equations ◽  
Integral Equations ◽  
Fractional Differential Equations ◽  
Volterra Integral Equations ◽  
Nonlinear Fractional Differential Equations ◽  
Common Solution ◽  
Fractional Differential

Common fixed point results under w-distance with applications to nonlinear integral equations and nonlinear fractional Differential Equations

2021 ◽  
Vol 71 (6) ◽  
pp. 1511-1528
Author(s):  
D. Ramesh Kumar
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Common Fixed Point ◽  
Integral Equations ◽  
Fractional Differential Equations ◽  
Distance Functions ◽  
Fredholm Integral Equations ◽  
Nonlinear Fractional Differential Equations ◽  
Contraction Condition ◽  
Fractional Differential

Abstract In this article, we prove some new common fixed point results under the generalized contraction condition using w-distance and weak altering distance functions. Also, the validity of the results is demonstrated by an example along with numerical experiment for approximating the common fixed point. Later, as applications, the unique common solutions for the system of nonlinear Fredholm integral equations, nonlinear Volterra integral equations and nonlinear fractional differential equations of Caputo type are derived.

scholarly journals Implicit nonlinear fractional differential equations of variable order

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Amar Benkerrouche ◽  
Mohammed Said Souid ◽  
Kanokwan Sitthithakerngkiet ◽  
Ali Hakem
Keyword(s):  
Differential Equations ◽  
Boundary Value Problem ◽  
Fractional Differential Equations ◽  
Boundary Value ◽  
Variable Order ◽  
Stability Of Solutions ◽  
Nonlinear Fractional Differential Equations ◽  
Caputo Fractional Differential Equations ◽  
Fractional Differential ◽  
The Stability

AbstractIn this manuscript, we examine both the existence and the stability of solutions to the implicit boundary value problem of Caputo fractional differential equations of variable order. We construct an example to illustrate the validity of the observed results.

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