Existence and H-U Stability of Solution for Coupled System of Fractional-Order with Integral Conditions Involving Caputo-Hadamard Derivatives, Hadamard Integrals by Muath Awadalla, Muthaian Subramanian, Murugesan Manigandan, Kinda Abuasbeh

“…In this article, the primary focus of our study is to investigate the existence, uniqueness, and Ulam-Hyers stability results for coupled fractional differential equations of the Caputo-Hadamard type that are supplemented with Hadamard integral boundary conditions. …”
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A Study of Caputo-Hadamard-Type Fractional Differential Equations with Nonlocal Boundary Conditions by Wafa Shammakh

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The Hadamard-PINN for PDE inverse problems: Convergence with distant initial guesses by Yohan Chandrasukmana, Helena Margaretha, Kie Van Ivanky Saputra

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Nonlinear Langevin Equation of Hadamard-Caputo Type Fractional Derivatives with Nonlocal Fractional Integral Conditions by Jessada Tariboon, Sotiris K. Ntouyas, Chatthai Thaiprayoon

“…We study existence and uniqueness of solutions for a problem consisting of nonlinear Langevin equation of Hadamard-Caputo type fractional derivatives with nonlocal fractional integral conditions. …”
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Existence and Uniqueness for a System of Caputo-Hadamard Fractional Differential Equations with Multipoint Boundary Conditions by S. Nageswara Rao, Ahmed Hussein Msmali, Manoj Singh, Abdullah Ali H. Ahmadini

“…In this paper, we study existence and uniqueness of solutions for a system of Caputo-Hadamard fractional differential equations supplemented with multi-point boundary conditions. …”
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Existence and Uniqueness Results for Hadamard-Type Fractional Differential Equations with Nonlocal Fractional Integral Boundary Conditions by Phollakrit Thiramanus, Sotiris K. Ntouyas, Jessada Tariboon

“…We study the existence and uniqueness of solutions for a fractional boundary value problem involving Hadamard-type fractional differential equations and nonlocal fractional integral boundary conditions. …”
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Some sufficient conditions for univalence by Sukhjit Singh

“…A new subclass R(α), 0≤α≤1, of the class St(1/2) the class of starlike functions of order 1/2 is introduced and it is shown that R(α) is closed with respect to the Hadamard product of analytic functions. Some sufficient conditions for the normalized regular functions to be univalent in the unit disk E are given.…”
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On Mixed Equilibrium Problems in Hadamard Spaces by Chinedu Izuchukwu, Kazeem Olalekan Aremu, Olawale Kazeem Oyewole, Oluwatosin Temitope Mewomo, Safeer Hussain Khan

“…The main purpose of this paper is to study mixed equilibrium problems in Hadamard spaces. First, we establish the existence of solution of the mixed equilibrium problem and the unique existence of the resolvent operator for the problem. …”
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Implicit Methods for Equilibrium Problems on Hadamard Manifolds by Muhammad Aslam Noor, Saira Zainab, Yonghong Yao

“…We use the auxiliary principle technique to suggest and analyze an implicit method for solving the equilibrium problems on Hadamard manifolds. The convergence of this new implicit method requires only the speudomonotonicity, which is a weaker condition than monotonicity. …”
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Existence Results of Langevin Equations with Caputo–Hadamard Fractional Operator by Sombir Dhaniya, Anoop Kumar, Aziz Khan, Thabet Abdeljawad, Manar A. Alqudah

“…In this manuscript, we deal with a nonlinear Langevin fractional differential equation that involves the Caputo–Hadamard and Caputo fractional operators, with nonperiodic and nonlocal integral boundary conditions. …”
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Hilfer-Hadamard Nonlocal Integro-Multipoint Fractional Boundary Value Problems by Chanon Promsakon, Sotiris K. Ntouyas, Jessada Tariboon

“…This paper is concerned with the existence and uniqueness of solutions for a new class of boundary value problems, consisting by Hilfer-Hadamard fractional differential equations, supplemented with nonlocal integro-multipoint boundary conditions. …”
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New extensions version of Hermite–Hadamard type inequalities by means of conformable fractional integrals by Umut Bas, Hüseyin Budak, Hasan Kara

“…What’s more, we prove the Hermite-Hadamard inequality, which includes conformable fractional integrals, with the aid of condition f′(a+b−t)−f′(t)≥0,t∈ [a,a+b2]…”
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Existence and Ulam–Hyers stability results for Caputo–Hadamard fractional differential equations with non-instantaneous impulses by Mesfin Teshome Beyene, Mitiku Daba Firdi, Tamirat Temesgen Dufera

“…Abstract In this manuscript, we investigated the existence, uniqueness, and Ulam–Hyers stability results of solutions to implicit Caputo–Hadamard fractional differential equations with noninstantaneous impulses and δ − d e r i v a t i v e $\delta -derivative$ initial conditions. …”
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A Generalization of Hermite–Hadamard–Fejer Type Inequalities for the p-Convex Function via α-Generator by Erdal Ünlüyol, Yeter Erdaş

“…Third, we get some new theorems using Hermite–Hadamard–Fejer inequality for the αp-convex function. …”
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On the Ulam stability and existence of $ L^p $-solutions for fractional differential and integro-differential equations with Caputo-Hadamard derivative by Abduljawad Anwar, Shayma Adil Murad

“…In this paper, we investigate the existence and uniqueness of $ L^p $-solutions for nonlinear fractional differential and integro-differential equations with boundary conditions using the Caputo-Hadamard derivative. By employing Hölder's inequality together with the Krasnoselskii fixed-point theorem and the Banach contraction principle, the study establishes sufficient conditions for solving nonlinear problems. …”
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On close-to-convex functions of complex order by H. S. Al-Amiri, Thotage S. Fernando

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ON SOLVABILITY OF SOME BOUNDARY-VALUE PROBLEMS FOR THE NON-LOCAL POISS by B. Kh. Turmetov

“…In the studied problems, the boundary conditions involve fractional-order operators with derivatives of the Hadamard type. …”
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Some well-known inequalities of Ostrowski like for Caputo derivatives by Yonghong Liu, Ghulam Farid, Jongsuk Ro, Mawahib Elamin, Sayed Abdel-Khalek

“…This paper aims to provide new versions of some known inequalities by applying Caputo fractional derivatives. Ostrowski, Hermite-Hadamard and Ostrowski-Grüss-type inequalities are given. …”
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On a More Accurate Half-Discrete Mulholland-Type Inequality Involving One Multiple Upper Limit Function by Xianyong Huang, Bicheng Yang

“…By the use of the weight functions, the symmetry property, and Hermite-Hadamard’s inequality, a more accurate half-discrete Mulholland-type inequality involving one multiple upper limit function is given. …”
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Using a Divergence Regularization Method to Solve an Ill-Posed Cauchy Problem for the Helmholtz Equation by Benedict Barnes, Anthony Y. Aidoo, Joseph Ackora-Prah

“…As a result, DRM restores all three Hadamard requirements for well-posedness.…”
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