Analisis Nikah Siri Dalam Perspektif Psikologi Dan Sosiologi Hukum Keluarga Islam

Penelitian ini merupakan sebuah analisis mendalam terhadap fenomena pernikahan siri dalam konteks hukum keluarga Islam, dengan pendekatan psikologi dan sosiologi. Pernikahan siri, meskipun secara hukum kerap dianggap kontroversial, tetap menjadi praktik yang signifikan dalam masyarakat yang menganut Islam. Penelitian ini bertujuan untuk memahami faktor-faktor psikologis dan sosial yang memengaruhi keputusan individu untuk melakukan pernikahan siri, serta dampaknya terhadap struktur keluarga dan masyarakat secara lebih luas. Dalam analisis psikologis, penelitian ini akan menggali motivasi dan faktor-faktor emosional yang mendorong individu untuk memilih pernikahan siri sebagai alternatif dalam memenuhi kebutuhan mereka dalam konteks hubungan intim. Sementara dalam analisis sosiologis, penelitian ini akan memeriksa dampak sosial dan normatif dari pernikahan siri terhadap struktur sosial masyarakat Islam, termasuk bagaimana hal ini memengaruhi status perempuan dan anak-anak dalam keluarga dan masyarakat.Hasil penelitian ini diharapkan akan memberikan wawasan yang lebih baik tentang fenomena pernikahan siri dalam masyarakat Islam, serta menyediakan dasar bagi perubahan dan penyempurnaan hukum keluarga Islam yang relevan dengan realitas sosial dan psikologis yang berkembang. Penelitian ini juga dapat menjadi acuan untuk pemahaman yang lebih baik tentang bagaimana praktik pernikahan siri dapat diintegrasikan atau diatur lebih baik dalam kerangka hukum dan norma-norma sosial yang ada.

Inverse Problems for Some Fractional Differential Equations

Inverse Problems for Some Fractional Differential Equations Fractional Calculus(FC) is about the investigation of arbitrary order derivatives, integrals, special functions and equations involving these operators. This subject has its roots back to late seventeenth century. In recent years scientists and engineers are using it rigorously as it provides an efficient method to model many well known physical phenomenon when compared with their counterpart (integer order calculus). For example, fractional order diffusion/transport equation has been used to explain anomalies in diffusion/transport process which occurs in many physical situations such as transport in heterogenous or porous media. For a physical process scientists are interested in the investigations of causes and effectsofthatphysicalprocess. Theeffectsofanyphysicalprocess(usuallyknown as direct problems) are easier to study then the causes that forces the system to behave in a particular manner. The mathematical models in which we study the causes are termed as inverse problems(IPs). The field of IPs investigates how to convert measurements into information about a physical process. The field of IPs is of great interest as it has many applications just to mention a few are in medical imaging, acoustic, heat conduction, source identification in a stream, shape optimization etc. In this thesis, we have studied time, space as well as space-time fractional differential equations. Through out our research investigation we have used fractional derivatives defined in the sense of Hilfer and Caputo. It is to be noted that Hilfer fractional derivative (HFD) interpolates both Riemann-Liouville(RLFD) and Caputo fractional derivatives(CFD) for particular choices of parameters. For a fourth order time fractional differential equation(TFDE) with nonlocal boundary conditions(knownasSmaraskii-Ionkinboundaryconditions)involvingHilferfractionalderivative(HFD),twoinversesourceproblems(ISPs)areconsidered. ISPof determining a space dependent source term for a TFDE in two space dimensions is also considered. Existence, uniqueness and stability results for the ISPs are proved under certain regularity conditions on the given data. For a multi-term TFDE involving HFDs ISP of recovering a time dependent source term is studied by using Heaviside-Mikusinski’s operational calculus approach. The spectral problem is non-self-adjoint and a bi-orthogonal system of functions(BSFs) is used toconstructtheseriessolutionoftheISPs. Foraspace-timefractionaldifferential equation(STFDE)withDirichletzeroboundaryconditionsalongwithappropriate over-specified conditions two ISPs of recovering space and time dependent sources are considered. In the last research problem of this thesis inverse coefficient problem(ICP)foraspacefractionaldifferentialequation(SFDE)isstudied. Weproved existence, uniqueness and stability results for the solution of the considered IPs by imposing certain regularity conditions on the given datum.