Browsing by Author "Sahoo, Soubhagya Kumar"

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Citation Count: Botmart, Thongchai...et.al. (2023). "Certain midpoint-type Feje acute accent r and Hermite-Hadamard inclusions involving fractional integrals with an exponential function in kernel", AIMS Mathematics, Vol.8, No.3, pp.5616-5638.
Certain midpoint-type Feje acute accent r and Hermite-Hadamard inclusions involving fractional integrals with an exponential function in kernel
(2023) Botmart, Thongchai; Sahoo, Soubhagya Kumar; Kodamasingh, Bibhakar; Latif, Muhammad Amer; Jarad, Fahd; Kashuri, Artion; 234808
In this paper, using positive symmetric functions, we offer two new important identities of fractional integral form for convex and harmonically convex functions. We then prove new variants of the Hermite-Hadamard-Fejer type inequalities for convex as well as harmonically convex functions via fractional integrals involving an exponential kernel. Moreover, we also present improved versions of midpoint type Hermite-Hadamard inequality. Graphical representations are given to validate the accuracy of the main results. Finally, applications associated with matrices, q-digamma functions and modifed Bessel functions are also discussed.
Citation Count: Botmart, Thongchai...et.al. (2023). "Certain midpoint-type Fejer and Hermite-Hadamard inclusions involving fractional integrals with an exponential function in kernel (vol 8, pg 5616, 2023)", AIMS Mathematics, Vol.8, No.6, pp.13785-13786.
Certain midpoint-type Fejer and Hermite-Hadamard inclusions involving fractional integrals with an exponential function in kernel (vol 8, pg 5616, 2023)
(2023) Botmart, Thongchai; Sahoo, Soubhagya Kumar; Kodamasingh, Bibhakar; Latif, Muhammad Amer; Jarad, Fahd; Kashuri, Artion; 234808
Citation Count: Sahoo, Soubhagya Kumar;...et.al. (2022). "Hermite-Hadamard type inclusions via generalized Atangana-Baleanu fractional operator with application", AIMS Mathematics, Vol.7, No.7, pp.12303-12321.
Hermite-Hadamard type inclusions via generalized Atangana-Baleanu fractional operator with application
(2022) Sahoo, Soubhagya Kumar; Jarad, Fahd; Kodamasingh, Bibhakar; Kashuri, Artion; 234808
Defining new fractional operators and employing them to establish well-known integral inequalities has been the recent trend in the theory of mathematical inequalities. To take a step forward, we present novel versions of Hermite-Hadamard type inequalities for a new fractional operator, which generalizes some well-known fractional integral operators. Moreover, a midpoint type fractional integral identity is derived for differentiable mappings, whose absolute value of the first-order derivatives are convex functions. Moreover, considering this identity as an auxiliary result, several improved inequalities are derived using some fundamental inequalities such as Hölder-İşcan, Jensen and Young inequality. Also, if we take the parameter ρ = 1 in most of the results, we derive new results for Atangana-Baleanu equivalence. One example related to matrices is also given as an application.
Citation Count: Srivastava, Hari Mohan;...et.al. (2022). "Hermite–Hadamard Type Inequalities for Interval-Valued Preinvex Functions via Fractional Integral Operators", International Journal of Computational Intelligence Systems, Vol.15, No.1.
Hermite–Hadamard Type Inequalities for Interval-Valued Preinvex Functions via Fractional Integral Operators
(2022) Srivastava, Hari Mohan; Sahoo, Soubhagya Kumar; Mohammed, Pshtiwan Othman; Baleanu, Dumitru; Kodamasingh, Bibhakar; 56389
In this article, the notion of interval-valued preinvex functions involving the Riemann–Liouville fractional integral is described. By applying this, some new refinements of the Hermite–Hadamard inequality for the fractional integral operator are presented. Some novel special cases of the presented results are discussed as well. Also, some examples are presented to validate our results. The established outcomes of our article may open another direction for different types of integral inequalities for fractional interval-valued functions, fuzzy interval-valued functions, and their associated optimization problems.
Citation Count: Mohammed, Pshtiwan Othman;...et.al. (2023). "Monotonicity and positivity analyses for two discrete fractional-order operator types with exponential and Mittag–Leffler kernels", Journal of King Saud University - Science, Vol35, No.7.
Monotonicity and positivity analyses for two discrete fractional-order operator types with exponential and Mittag–Leffler kernels
(2023) Mohammed, Pshtiwan Othman; Srivastava, Hari Mohan; Baleanu, Dumitru; Al-Sarairah, Eman; Sahoo, Soubhagya Kumar; Chorfi, Nejmeddine; 56389
The discrete analysed fractional operator technique was employed to demonstrate positive findings concerning the Atangana-Baleanu and discrete Caputo-Fabrizo fractional operators. Our tests utilized discrete fractional operators with orders between 1<φ<2, as well as between 1<φ<[Formula presented]. We employed the initial values of Mittag–Leffler functions and applied the principle of mathematical induction to ensure the positivity of the discrete fractional operators at each time step. As a result, we observed a significant impact of the positivity of these operators on ∇Q(τ) within Np0+1 according to the Riemann–Liouville interpretation. Furthermore, we established a correlation between the discrete fractional operators based on the Liouville-Caputo and Riemann–Liouville definitions. In addition, we emphasized the positivity of ∇Q(τ) in the Liouville-Caputo sense by utilizing this relationship. Two examples are presented to validate the results.
Citation Count: Jarad, Fahd;...et.al. (2023). "New stochastic fractional integral and related inequalities of Jensen–Mercer and Hermite–Hadamard–Mercer type for convex stochastic processes", Journal of Inequalities and Applications, Vol.2023, no.1.
New stochastic fractional integral and related inequalities of Jensen–Mercer and Hermite–Hadamard–Mercer type for convex stochastic processes
(2023) Jarad, Fahd; Sahoo, Soubhagya Kumar; Nisar, Kottakkaran Sooppy; Treanţă, Savin; Emadifar, Homan; Botmart, Thongchai; 234808
In this investigation, we unfold the Jensen–Mercer (J− M) inequality for convex stochastic processes via a new fractional integral operator. The incorporation of convex stochastic processes, the J− M inequality and a fractional integral operator having an exponential kernel brings a new direction to the theory of inequalities. With this in mind, estimations of Hermite–Hadamard–Mercer (H− H− M)-type fractional inequalities involving convex stochastic processes are presented. In the context of the new fractional integral operator, we also investigate a novel identity for differentiable mappings. Then, a new related H− H− M-type inequality is presented using this identity as an auxiliary result. Applications to special means and matrices are also presented. These findings are particularly appealing from the perspective of optimization, as they provide a larger context to analyze optimization and mathematical programming problems.
Citation Count: Mohammed, Pshtiwan Othman;...ET.AL. (2023). "Positivity analysis for mixed order sequential fractional difference operators", AIMS Mathematics, Vol.8, No.2, pp.2673-2685.
Positivity analysis for mixed order sequential fractional difference operators
(2023) Mohammed, Pshtiwan Othman; Baleanu, Dumitru; Abdeljawad, Thabet; Sahoo, Soubhagya Kumar; Abualnaja, Khadijah M.; 56389
We consider the positivity of the discrete sequential fractional operators( RL a0 +1∇ν1 defined on the set D1 (see (1.1) and Figure 1) and( RL a0 +2∇ν1 RL a0 ∇ν2 f) (τ) RL a0 ∇ν2 f) (τ) of mixed order defined on the set D2 (see (1.2) and Figure 2) for τ ∈ Na0 . By analysing the first sequential operator, we reach that (∇f )(τ)≧ 0, for each τ∈ Na0 +1. Besides, we obtain(∇ f)(3) ≧ 0 by analysing the second sequential operator. Furthermore, some conditions to obtain the proposed monotonicity results are summarized. Finally, two practical applications are provided to illustrate the efficiency of the main theorems.
Citation Count: Tariq, Muhammad...et al. (2021). "Some integral inequalities for generalized preinvex functions with applications", AIMS MATHEMATICS, Vol. 6, No. 12, pp. 13907-13930.
Some integral inequalities for generalized preinvex functions with applications
(2021) Tariq, Muhammad; Sahoo, Soubhagya Kumar; Jarad, Fahd; Kodamasingh, Bibhakar; 234808
The main objective of this work is to explore and characterize the idea of s-type preinvex function and related inequalities. Some interesting algebraic properties and logical examples are given to support the newly introduced idea. In addition, we attain the novel version of Hermite-Hadamard type inequality utilizing the introduced preinvexity. Furthermore, we establish two new identities, and employing these, we present some refinements of Hermite-Hadamard-type inequality. Some special cases of the presented results for di fferent preinvex functions are deduced as well. Finally, as applications, some new inequalities for the arithmetic, geometric and harmonic means are established. Results obtained in this paper can be viewed as a significant improvement of previously known results. The awe-inspiring concepts and formidable tools of this paper may invigorate and revitalize for additional research in this worthy and absorbing field.