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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 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 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]

In this paper, we formulate a new set of sufficient conditions for the approximate controllability of fractional evolution stochastic integrodifferential delay inclusions of order r ∈ (1 , 2) with nonlocal conditions in Hilbert space. Martelli's fixed point theorem, multivalued functions, cosine and sine families, fractional calculus and operator semigroups are used to establish the results under the assumption that the corresponding linear system is approximately controllable. Finally, an example is provided to illustrate the applicability of the obtained theoretical results. [ABSTRACT FROM AUTHOR]

• This manuscript is mainly focusing on the approximate controllability of Hilfer fractional neutral stochastic integro-differential equations. • The principal results of this article are proved based on the theoretical concepts related to the fractional calculus and Schauder's fixed-point theorem. • Initially, we discuss the approximate controllability of the fractional evolution system. • Then, we extend our results to the concept of nonlocal conditions. • Finally, we provide theoretical and practical applications to assist in the effectiveness of the discussion. This manuscript is mainly focusing on the approximate controllability of Hilfer fractional neutral stochastic integro-differential equations. The principal results of this article are proved based on the theoretical concepts related to the fractional calculus and Schauder's fixed-point theorem. Initially, we discuss the approximate controllability of the fractional evolution system. Then, we extend our results to the concept of nonlocal conditions. Finally, we provide theoretical and practical applications to assist in the effectiveness of the discussion. [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]