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In this article, we consider integro-differential equations involving the recently explored Atangana–Baleanu fractional derivatives which contain the generalized Mittag-Leffler functions in their kernels. Utilizing fixed point techniques, we examine the existence and uniqueness of solutions to such equations in Banach spaces. Moreover, we consider an example and investigate numerical outcomes for various values of the fractional order. Then, we consider the stability of the tackled integro-differential equation in the frame of Ulam. [ABSTRACT FROM AUTHOR]

Abstract This article deals with the use of Krasnoselskii's fixed point theorem and Leray–Schauder alternative theorem combined with resolvent operator and some analytical methods to investigate the exact controllability and continuous dependence of a class of neutral fractional integro-differential systems with state-dependent delay in Banach spaces. An application to exemplify the concept is provided at the end. [ABSTRACT FROM AUTHOR]

In this paper, we examine the multi-derivative nonlinear fractional integro-differential equations involving Atangana-Baleanu fractional derivative of Riemann-Liouville sense. We study the elementary results about the existence and difference solution on different data, based on T. R. Prabhakar fractional integral operator ε σ , η , ϑ ; c + γ involving generalized Mittag-Leffler function. The results are obtained by using Krasnoselskii's fixed point theorem and Gronwall-Bellman inequality. 2010 Subject Classification: 34A60,33E12,34G20. • The existence outcomes for fractional multi-derivative nonlinear integrodifferential equations involving A-B fractional derivative of R-L sense. • We study the elementary results about the existence and difference solution on different data, based on T. R. Prabhakar fractional integral operator. • The results are obtained by using Krasnoselskii's fixed point theorem and Gronwall-Bellman inequality. [ABSTRACT FROM AUTHOR]

This article concerning to initiate the existence of solutions via fixed point technique for: 1. The Atangana–Baleanu Willis Aneurysm System { 0 AB D t n 1 p = q 0 AB D t n 2 q = F cos (w t) − ψ q − a p + b p 2 − c p 3 where n 1 > 0 , n 2 < 2. 2. Singular perturbations of boundary value problems for non- linear fuzzy differential equations of the second order { ϵ U ″ (p) = Θ (p , U (p) , U ′ (p)) ; 0 < p < 1 with U (0) = θ 1 U (1) = θ 2 where θ 1 , θ 2 ∈ I , here I = 0 , 1 , ϵ represents a small parameter and Θ : I × M × M → F (M) is a smooth function. [ABSTRACT FROM AUTHOR]

In this article, we study an impulsive neutral fractional integro-differential equation (FIDE) via Atangana-Baleanu fractional derivative. The fixed point approach is employed to prove the existence results of the equation with initial and non-local conditions. The application of the results obtained are verified using suitable examples of different fractional orders. [ABSTRACT FROM AUTHOR]

• The neutral fractional delay system governed by nonlocal conditions is presented and proved. • Noncompact measure and Mönch's technique, fractional calculus techniques are used. • Established the sufficient conditions to confirm the existence of neutral delay differential system. • An illustration of derived results is given. The study of neutral fractional delay system governed by nonlocal conditions is presented and proved. With the aid of fractional theory, noncompact measure and Mönch's technique, we established some sufficient conditions to confirm the existence of neutral delay differential system. An illustration of derived results is also offered. [ABSTRACT FROM AUTHOR]

In this manuscript, we describe fractional differential equations with neutral, integral boundary conditions and mixed delay using Atangana–Baleanu derivatives, which include the generalized Mittag-Leffler kernel. We determine the existence and uniqueness of results and analysis by fixed point method. Moreover, we explained the stability of the fractional differential equation in the frame of Ulam–Hyers. Then, we investigate an example with various values and illustrate the outcomes graphically. • We consider the nonlinear fractional mixed integro-differential equations with fractional boundary conditions. • The existence result is obtained by using standard fixed point theory. • An example is given to illustrate our analytical and numerical results. By using MATLAB coding graph is drawn. [ABSTRACT FROM AUTHOR]

In this article, we examine a nonlinear impulsive neutral fractional differential equation with nonlocal condition in an arbitrary Hilbert space. We obtain an associated integral equation and then consider a sequence of approximate integral equations by the projection of considered associated nonlocal neutral fractional integral equation onto finite dimensional space. The existence and uniqueness of an approximate solution by using analytic semigroup theory and the Fixed-point method are demonstrated. Convergence of the solutions of the approximate integral equation is proved. The Faedo-Galerkin approximation of the solution is studied and demonstrated some convergence results. Lastly, the application is presented to illustrate the theory of the main results. [ABSTRACT FROM AUTHOR]

This paper involves complex valued versions of Riemann-Liouville integral, Atangana-Baleanu integral operator and non-linear Telegraph equation. Under various suitable assumptions the results are established in the setting of complex valued double controlled metric space. Thereafter, by making consequent use of the fixed point method, short and simple proofs are obtained for solutions of Riemann-Liouville integral, complex valued Atangana-Baleanu integral operator and non-linear Telegraph equation. [ABSTRACT FROM AUTHOR]

This study is devoted to developing mathematical models associated with the Helmholtz equation as a second-order oscillator involved with nonlinear Caputo fractional difference equations. This study also focuses on determining the approximate solution of this model via the Ulam stability conception. Some properties of the mathematical model dealt with in this study are also presented. Numerical simulations are presented to justify the existence of stability results. • A new formulation of the mathematical model and analysis in Helmholtz Duffing oscillator with the damping term is presented. on the natural frequencies. • Using this Helmholtz–Duffing oscillator with the damping term, we proved the Hyers–Ulam stability to ensure existence and uniqueness. • We analyzed practical examples describing the application of quadcopter. [ABSTRACT FROM AUTHOR]

• A non-linear Hilfer system has been studied for mild solution with the aid of Banach contraction principle. • Mönch fixed point theorem ensures the exact controllability of the system concerned. • Existence of optimal pair verified for the Hilfer nonlinear system. • Some numerical approaches have been done to exemplify the criteria of obtained results using the software 'mathematica'. • Comparison analysis was done with the major classifications of fractional systems. In this article, the controllability results of the non-dense Hilfer neutral fractional derivative (HNFD) are presented. The results are acknowledged using semigroup theory, fractional calculus, Banach contraction principle, and Mönch technique. Moreover, a numerical analysis is given to enhance our model. [ABSTRACT FROM AUTHOR]