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This article explores the existence and approximate controllability of integral solutions for Hilfer fractional evolution equations in a non-dense domain. Leveraging the well-known generalized Banach contraction theorem, we establish both the existence and uniqueness of the integral solution. Furthermore, we adopt a sequential approach to derive results related to approximate controllability, without relying on the compactness of semigroups or the uniform boundedness of nonlinear functions. To validate our findings, we present and discuss an illustrative example. [ABSTRACT FROM AUTHOR]

Abstract In this article, we focus on studying the Duffing problem with the time delay of pantograph type via the Hilfer fractional derivatives on the infinite interval ( 0 , ∞ ) $(0,\infty )$ . An appropriate Banach space supported with the Bielecki norm in the Mittag–Leffler function sense is introduced for new and convenient analysis. The existence and uniqueness ( E & U $\mathbf{E\&U}$ ) of the solutions are proved by utilizing the classical fixed point theorems (FPT s). Moreover, the Hyers–Ulam (HU) stability is discussed for our Hilfer fractional Duffing pantograph system (HFDPS). Ultimately, our results are enhanced by providing numerical examples with graphics simulations to check the validity of the main outcomes.

In this article, we focus on studying the Duffing problem with the time delay of pantograph type via the Hilfer fractional derivatives on the infinite interval (0 , ∞) . An appropriate Banach space supported with the Bielecki norm in the Mittag–Leffler function sense is introduced for new and convenient analysis. The existence and uniqueness ( E & U ) of the solutions are proved by utilizing the classical fixed point theorems (FPTs). Moreover, the Hyers–Ulam (HU) stability is discussed for our Hilfer fractional Duffing pantograph system (HFDPS). Ultimately, our results are enhanced by providing numerical examples with graphics simulations to check the validity of the main outcomes. [ABSTRACT FROM AUTHOR]

We consider an inverse problem for diffusion equation involving fractional Laplacian operator in space and Hilfer fractional derivatives in time with Dirichlet zero boundary conditions. The inverse problem is to recover time-dependent source term and diffusion concentration with an integral type over-determination condition. We discuss the analytical solution of the inverse problem and prove the existence and uniqueness of the analytical solution. Some special cases and examples for the considered inverse problem are provided. [ABSTRACT FROM AUTHOR]

The Levin-Nohel equations play key roles in the interpretation of real phenomena and have interesting applications in engineering and science areas, such as mathematical physics, mathematical biology, image processing, and numerical analyses. This article investigates a new structure for the delay neutral Levin-Nohel integrodifferential (NLNID) system via a Hilfer fractional derivative and is supplemented by initial and instantaneous impulse conditions. A fractional integral equation corresponding to the proposed system is derived and used to prove the existence and uniqueness of the solution with the help of the Banach contraction principle. Additionally, the Ulam-Hyers-Mittag-Leffler (UHML) stability is studied by utilizing the generalized Gronwall's inequality and nonlinear analysis issues. As a consequence, the Ulam-Hyers (UH) stability and generalized UH are also deduced. Furthermore, the Riemann-Liouville ($ \mathcal{R.L.} $) and Caputo fractional versions of the proposed system are discussed. Finally, numerical applications supported with tables and graphics are provided to test the exactitude of the findings.

The Levin-Nohel equations play key roles in the interpretation of real phenomena and have interesting applications in engineering and science areas, such as mathematical physics, mathematical biology, image processing, and numerical analyses. This article investigates a new structure for the delay neutral Levin-Nohel integrodifferential (NLNID) system via a Hilfer fractional derivative and is supplemented by initial and instantaneous impulse conditions. A fractional integral equation corresponding to the proposed system is derived and used to prove the existence and uniqueness of the solution with the help of the Banach contraction principle. Additionally, the Ulam-Hyers-Mittag-Leffler (UHML) stability is studied by utilizing the generalized Gronwall's inequality and nonlinear analysis issues. As a consequence, the Ulam-Hyers (UH) stability and generalized UH are also deduced. Furthermore, the Riemann-Liouville ( R. L. ) and Caputo fractional versions of the proposed system are discussed. Finally, numerical applications supported with tables and graphics are provided to test the exactitude of the findings. The Levin-Nohel equations play key roles in the interpretation of real phenomena and have interesting applications in engineering and science areas, such as mathematical physics, mathematical biology, image processing, and numerical analyses. This article investigates a new structure for the delay neutral Levin-Nohel integrodifferential (NLNID) system via a Hilfer fractional derivative and is supplemented by initial and instantaneous impulse conditions. A fractional integral equation corresponding to the proposed system is derived and used to prove the existence and uniqueness of the solution with the help of the Banach contraction principle. Additionally, the Ulam-Hyers-Mittag-Leffler (UHML) stability is studied by utilizing the generalized Gronwall's inequality and nonlinear analysis issues. As a consequence, the Ulam-Hyers (UH) stability and generalized UH are also deduced. Furthermore, the Riemann-Liouville ( ) and Caputo fractional versions of the proposed system are discussed. Finally, numerical applications supported with tables and graphics are provided to test the exactitude of the findings. [ABSTRACT FROM AUTHOR]

This article investigates time optimal controls for the Cauchy problem of Hilfer fractional evolution equations. At first, by employing the fixed point technique and the operator semigroup theory, an existence theorem is obtained. Then the existence of time optimal control pair is studied by applying an approximate technique. An example is given as applications in the last section. [ABSTRACT FROM AUTHOR]

In this paper, the existence, uniqueness, compactness, and stability of a coupled random diffierential equations involving the Hilfer fractional derivatives with nonlocal boundary conditions are discussed. Arguments are discussed via some random fixed point theorems in a separable vector Banach spaces and Ulam type stability. Some examples are presented to ensure the abstract results. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the concept of regional enlarged observability (ReEnOb) for fractional differential equations (FDEs) with the Hilfer derivative. To proceed this, we develop an approach based on the Hilbert uniqueness method (HUM). We mainly reconstruct the initial state ν 0 1 on an internal subregion ω from the whole domain Ω with knowledge of the initial information of the system and some given measurements. This approach shows that it is possible to obtain the desired state between two profiles in some selective internal subregions. Our findings develop and generalize some known results. Finally, we give two examples to support our theoretical results. [ABSTRACT FROM AUTHOR]

In this manuscript the controllability of Hilfer fractional neutral differential inclusions with non-instantaneous impulse in Banach space is investigated by using semi-group theory, fractional calculus, upper semi-continuous (u.s.c), multi-functions and Mönch fixed point theorem. Sufficient conditions are derived by using Hausdorff measure of non-compactness (MNC). Further, the obtained result is illustrated by an example. [ABSTRACT FROM AUTHOR]

Abstract The main aim of this paper is to present some existence criteria for an infinite system of Hilfer fractional boundary value problems of the form D a + α , β u i = − F i ( t , u ) , u i ( a ) = u i ( b ) = 0 , a < t < b , i = 1 , 2 , … , $$ \mathcal{D}_{a^{+}}^{\alpha,\beta }u_{i}=-F_{i}(t,u),\quad u_{i}(a)=u_{i}(b)=0, a< t< b,i=1,2,\ldots, $$ in Banach sequence spaces of c 0 $c_{0}$ and l p , p ≥ 1 $l_{p},p\geq 1$ types. Our approach is based on the Darbo-type fixed point theorems acting on the condensing operators. The obtained existence results in each of the above sequence spaces are illustrated by presenting some numerical examples.

In this work, we investigate a class of nonlocal Volterra-Fredholm integro-differential equations involving Hilfer fractional derivatives and almost sectorial operators. We prove our results by applying Arzela-Ascoli theorem and Schauder's fixed point technique. Moreover, we show the fundamental properties of the representation of the solution by discussing a case related to the associated semigroup. For that, we consider compactness properties. [ABSTRACT FROM AUTHOR]

This paper is devoted to study the existence of a solution to Hilfer fractional differential equation with nonlocal boundary condition in Banach spaces. We use the equivalent integral equation to study the considered Hilfer differential problem with nonlocal boundary condition. The Mönch type fixed point theorem and the measure of the noncompactness technique are the main tools in this study. We demonstrate the existence of a solution with a suitable illustrative example. [ABSTRACT FROM AUTHOR]

The main aim of this paper is to present some existence criteria for an infinite system of Hilfer fractional boundary value problems of the form D a + α , β u i = − F i (t , u) , u i (a) = u i (b) = 0 , a < t < b , i = 1 , 2 , ... , in Banach sequence spaces of c 0 and l p , p ≥ 1 types. Our approach is based on the Darbo-type fixed point theorems acting on the condensing operators. The obtained existence results in each of the above sequence spaces are illustrated by presenting some numerical examples. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the controllability of nonlocal Hilfer-type fractional differential inclusions with noninstantaneous impulsive conditions in Banach spaces.

In this paper, we establish the existence of decay mild solutions on an unbounded interval of nonlocal fractional semilinear differential inclusions with noninstantaneous impulses and involving the Hilfer derivative. Our argument uses fixed point theorems, semigroup theory, multi-functions and a measure of noncompactness on the space of piecewise weighted continuous functions defined on an unbounded interval. An example is provided to illustrate our results.

The main objective of this paper is to present sufficient conditions for controllability of Hilfer fractional nonlinear stochastic systems in finite dimensional space. The main results are obtained by using the Nussbaum fixed point theorem, stochastic analysis approach and generalized fractional calculus (Hilfer fractional derivative) which is universality of Riemann-Liouville and Caputo fractional derivative. Finally, a numerical example is provided to show the effectiveness of the obtained theoretical result. The obtained result is more generalized one than the existing results on fractional stochastic system in finite dimensional space. [ABSTRACT FROM AUTHOR]

In this work, we investigate a class of nonlocal integro-differential equations involving Hilfer fractional derivatives and almost sectorial operators. We prove our results by applying Schauder’s fixed point technique. Moreover, we show the fundamental properties of the representation of the solution by discussing two cases related to the associated semigroup. For that, we consider compactness and noncompactness properties, respectively. Furthermore, an example is given to illustrate the obtained theory.