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‘Existence theory’ is a bold and imaginative contribution to social theory. Baert, Morgan and Ushiyama (hereafter ‘the authors’) draw on a broad range of existing approaches from Heidegger to Schutz to build a social theory that draws attention to time, the stages of life and the unavoidably precarious nature of human existence. At the same time, they pay careful attention to the social context in which time and existential precariousness combine to form what they call ‘the existential ladder’. Our lives are to some degree measured by the ‘existential milestones’ that we confront over time. These are not invariable stages, but they traditionally included entry into the work force, courtship and marriage, parenthood and maturity, and old age and death. There are in addition norms that attend these transitions. For example, procreation and parenthood are not for the elderly. Old fathers with young children are regarded as foolish if not reprehensible. Failure to pass through the milestones at the appropriate time may result in disappointments, stress and unhappiness.

This research work is devoted to undertaking a dynamical system representing SARS-CoV-19 disease under the concept of piecewise fractional-order derivative using the Caputo concept since long-memory and short-memory terms are not well explained by ordinary fractional differential equations. It has been found that for such disruption, piecewise operators of fractional derivatives have been found useful in many cases. Therefore, we study a compartmental model of susceptible and infected individuals under the concept of piecewise derivative. We establish the existence theory of the considered model by using some Banach and Schauder fixed-point theorems. Keeping the importance of stability, a pertinent result related to the said area is also developed. The said concept of stability is based on the concept given by Ulam and Hyers. Further, to derive the numerical results, we use the Euler method to develop a numerical scheme for the considered model. Using real available data, we have presented various graphical presentations of two compartments against different fractional orders and various values of isolation parameters. The crossover behaviors in the dynamics can be clearly observed, which is explained by the piecewise operators, not the usual fractional-order derivative.

This research work is related to studying a class of special type delay implicit fractional order differential equations under anti-periodic boundary conditions. With the help of classical fixed point theory due to Schauder and Banach, we derive some results about the existence of at least one solution. Further, we also study some results including Hyers–Ulam, generalized Hyers–Ulam, Hyers–Ulam Rassias, and generalized Hyers–Ulam–Rassias stability. We provide some test problems for illustrating our analysis.

This manuscript investigates an extended boundary value problem for a fractional pantograph differential equation with instantaneous impulses under the Caputo proportional fractional derivative with respect to another function. The solution of the proposed problem is obtained using Mittag–Leffler functions. The existence and uniqueness results of the proposed problem are established by combining the well-known fixed point theorems of Banach and Krasnoselskii with nonlinear functional techniques. In addition, numerical examples are presented to demonstrate our theoretical analysis.

We present some results on the existence, uniqueness and Hyers–Ulam stability to the solution of an implicit coupled system of impulsive fractional differential equations having Hadamard type fractional derivative. Using a fixed point theorem of Kransnoselskii’s type, the existence and uniqueness results are obtained. Along these lines, different kinds of Hyers–Ulam stability are discussed. An example is given to illustrate the main theorems.

This article is fundamentally concerned with deriving the solution formula, existence, and uniqueness of solutions of two types of Cauchy problems for impulsive fractional differential equations involving Atangana-Baleanu-Caputo (ABC) fractional derivative which possesses nonsingular Mittag-Leffler kernel. Our investigation is based on nonlinear functional analysis and some fixed point techniques. Besides, some examples are given delineated to illustrate the effectiveness of our outcome., Mathematics; Fractional impulsive problems; Atangana-Baleanu-Caputo operator; Existence theory; Fixed point theorem

In this paper, we establish sufficient conditions for the existence, uniqueness and Ulam&ndash, Hyers stability of the solutions of a coupled system of nonlinear fractional impulsive differential equations. The existence and uniqueness results are carried out via Banach contraction principle and Schauder&rsquo, s fixed point theorem. The main theoretical results are well illustrated with the help of an example.

This manuscript deals with the existence theory, uniqueness, and various kinds of Ulam&ndash, Hyers stability of solutions for a class and coupled system of fractional order differential equations involving Caputo derivatives. Applying Schaefer and Banach&rsquo, s fixed point approaches, existence and uniqueness results are obtained for the proposed problems. Stability results are investigated by using the classical technique of nonlinear functional analysis. Examples are given with each problem to illustrate the main results.

The paper presents the existence result for positive solutions of the differential equation $(g(x))''=f(t,x,(g(x))')$ satisfying the nonlocal boundary conditions $x(0)=x(T)$ , $\min\{ x(t): t \in J\}=0$ . Here the positive function $f$ satisfies local Caratheodory conditions on $[0,T] \times (0,\infty) \times (\R {\setminus} \{0\})$ and $f$ may be singular at the value 0 of both its phase variables. Existence results are proved by Leray-Schauder degree theory and Vitali's convergence theorem.

This paper establishes existence for semipositone (n, p) and conjugate discrete boundary value problems. Our analysis relies on Krasnoselskii's fixed-point theorem in a cone.

Existence theory of Filippov–Roxin type as well as a maximum principle for optimal control problem governed by nonlinear differential–algebraic equations of index 1, or 2, or 3 are formulated and proved. The index-3 case is illustrated on mechanical descriptor systems arising in robotics.

This paper presents analytical and numerical solutions of an optimal control problem for a quasilinear parabolic equation. The existence and uniqueness theorems of the solution are investigated. The derivation of formulae for the gradient of the modified cost function by solving the conjugated boundary value problem is explained. The numerical algorithm for solving the optimal control problem using partial quadratic interpolation technique is given. The computed optimal controls is helped to identify the unknown coefficients of the quasilinear parabolic equation. Numerical results are reported.

A general mixed multivalued mildly nonlinear variational inequality is considered. We establish an existence result for (GMMMNVIP) in H-spaces by using the new result of Chang et al [21].

A convective Cahn-Hilliard type equation of sixth order that describes the faceting of a growing surface is considered with periodic boundary conditions. By using a Galerkin approach the existence of weak solutions to this sixth order partial differential equation is established in $L^2(0,T; dot H^3_per)$. Furthermore stronger regularity results have been derived and these are used to prove uniqueness of the solutions. Additionally a numerical study shows that solutions behave similarly as for the better known convective Cahn-Hilliard equation. The transition from coarsening to roughening is analyzed, indicating that the characteristic length scale decreases logarithmically with increasing deposition rate.