In this paper, we introduce new concepts of a-type F-contractive mappings which are essentially weaker than the class of F-contractive mappings given in [21, 22] and different from a-GF-contractions given in [8]. Then...In this paper, we introduce new concepts of a-type F-contractive mappings which are essentially weaker than the class of F-contractive mappings given in [21, 22] and different from a-GF-contractions given in [8]. Then, sufficient conditions for the existence and uniqueness of fixed point are established for these new types of contractive mappings, in the setting of complete metric space. Consequently, the obtained results encompass various generalizations of the Banach contraction principle. Moreover, some examples and an application to nonlinear fractional differential equation are given to illustrate the usability of the new theory.展开更多
In the present manuscript, we propose the modification of Jain operators which the generalization of Szasz-Mirakyan operators. These new class operators are linear positive operators of discrete type depending on a re...In the present manuscript, we propose the modification of Jain operators which the generalization of Szasz-Mirakyan operators. These new class operators are linear positive operators of discrete type depending on a real parameters. We give theorem of degree of approximation and the Voronovskaya asymptotic formula.展开更多
This paper proposes a temporal-fractional porous medium model(T-FPMM)for describing the co-current and counter-current imbibition,which arises in a water-wet fractured porous media.The correlation be-tween the co-curr...This paper proposes a temporal-fractional porous medium model(T-FPMM)for describing the co-current and counter-current imbibition,which arises in a water-wet fractured porous media.The correlation be-tween the co-current and counter-current imbibition for the fractures and porous matrix are examined to determine the saturation and recovery rate of the reservoir.For different fractional orders in both porous matrix and fractured porous media,the homotopy analysis technique and its stability analysis are used to explore the parametric behavior of the saturation and recovery rates.Finally,the effects of wettability and inclination on the recovery rate and saturation are studied for distinct fractional values.展开更多
The nonlinear Kortewege-de Varies(KdV)equation is a functional description for modelling ion-acoustic waves in plasma,long internal waves in a density-stratified ocean,shallow-water waves and acoustic waves on a cryst...The nonlinear Kortewege-de Varies(KdV)equation is a functional description for modelling ion-acoustic waves in plasma,long internal waves in a density-stratified ocean,shallow-water waves and acoustic waves on a crystal lattice.This paper focuses on developing and analysing a resilient double parametric analytical approach for the nonlinear fuzzy fractional KdV equation(FFKdVE)under gH-differentiability of Caputo fractional order,namely the q-Homotopy analysis method with the Shehu transform(q-HASTM).A triangular fuzzy number describes the Caputo fractional derivative of orderα,0<α≤1,for modelling problem.The fuzzy velocity profiles with crisp and fuzzy conditions at different spatial positions are in-vestigated using a robust double parametric form-based q-HASTM with its convergence analysis.The ob-tained results are compared with existing works in the literature to confirm the efficacy and effectiveness of the method.展开更多
基金the support of CSIR,Govt.of India,Grant No.-25(0215)/13/EMR-II
文摘In this paper, we introduce new concepts of a-type F-contractive mappings which are essentially weaker than the class of F-contractive mappings given in [21, 22] and different from a-GF-contractions given in [8]. Then, sufficient conditions for the existence and uniqueness of fixed point are established for these new types of contractive mappings, in the setting of complete metric space. Consequently, the obtained results encompass various generalizations of the Banach contraction principle. Moreover, some examples and an application to nonlinear fractional differential equation are given to illustrate the usability of the new theory.
文摘In the present manuscript, we propose the modification of Jain operators which the generalization of Szasz-Mirakyan operators. These new class operators are linear positive operators of discrete type depending on a real parameters. We give theorem of degree of approximation and the Voronovskaya asymptotic formula.
文摘This paper proposes a temporal-fractional porous medium model(T-FPMM)for describing the co-current and counter-current imbibition,which arises in a water-wet fractured porous media.The correlation be-tween the co-current and counter-current imbibition for the fractures and porous matrix are examined to determine the saturation and recovery rate of the reservoir.For different fractional orders in both porous matrix and fractured porous media,the homotopy analysis technique and its stability analysis are used to explore the parametric behavior of the saturation and recovery rates.Finally,the effects of wettability and inclination on the recovery rate and saturation are studied for distinct fractional values.
文摘The nonlinear Kortewege-de Varies(KdV)equation is a functional description for modelling ion-acoustic waves in plasma,long internal waves in a density-stratified ocean,shallow-water waves and acoustic waves on a crystal lattice.This paper focuses on developing and analysing a resilient double parametric analytical approach for the nonlinear fuzzy fractional KdV equation(FFKdVE)under gH-differentiability of Caputo fractional order,namely the q-Homotopy analysis method with the Shehu transform(q-HASTM).A triangular fuzzy number describes the Caputo fractional derivative of orderα,0<α≤1,for modelling problem.The fuzzy velocity profiles with crisp and fuzzy conditions at different spatial positions are in-vestigated using a robust double parametric form-based q-HASTM with its convergence analysis.The ob-tained results are compared with existing works in the literature to confirm the efficacy and effectiveness of the method.
